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Journal articles on the topic 'Labeled graph'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

MATSUMOTO, KENGO. "FACTOR MAPS OF LAMBDA-GRAPH SYSTEMS AND INCLUSIONS OF C*-ALGEBRAS." International Journal of Mathematics 15, no. 04 (June 2004): 313–39. http://dx.doi.org/10.1142/s0129167x04002351.

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A λ-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In [Doc. Math. 7 (2002), 1–30], the author introduced a C*-algebra [Formula: see text] associated with a λ-graph system [Formula: see text] as a generalization of the Cuntz–Krieger algebras. In this paper, we study a functorial property between factor maps of λ-graph systems and inclusions of the associated C*-algebras with gauge actions. We prove that if there exists a surjective left-covering λ-graph system homomorphism [Formula: see text], there exists a unital embedding of the C*-algebra [Formula: see text] into the C*-algebra [Formula: see text] compatible to its gauge actions. We also show that a sequence of left-covering graph homomorphisms of finite labeled graphs gives rise to a λ-graph system such that the associated C*-algebra is an inductive limit of the Cuntz–Krieger algebras for the finite labeled graphs.

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2

Ishii, Atsushi. "The Markov theorems for spatial graphs and handlebody-knots with Y-orientations." International Journal of Mathematics 26, no. 14 (December 2015): 1550116. http://dx.doi.org/10.1142/s0129167x15501165.

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We establish the Markov theorems for spatial graphs and handlebody-knots. We introduce an IH-labeled spatial trivalent graph and develop a theory on it, since both a spatial graph and a handlebody-knot can be realized as the IH-equivalence classes of IH-labeled spatial trivalent graphs. We show that any two orientations of a graph without sources and sinks are related by finite sequence of local orientation changes preserving the condition that the graph has no sources and no sinks. This leads us to define two kinds of orientations for IH-labeled spatial trivalent graphs, which fit a closed braid, and is used for the proof of the Markov theorem. We give an enhanced Alexander theorem for orientated tangles, which is also used for the proof.

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3

Murugan, A. Nellai, and Shiny Priyanka. "TREE RELATED EXTENDED MEAN CORDIAL GRAPHS." International Journal of Research -GRANTHAALAYAH 3, no. 9 (September 30, 2015): 143–48. http://dx.doi.org/10.29121/granthaalayah.v3.i9.2015.2954.

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Let G = (V,E) be a graph with p vertices and q edges. A Extended Mean Cordial Labeling of a Graph G with vertex set V is a bijection from V to {0, 1,2} such that each edge uv is assigned the label where ⌈ x ⌉ is the least integer greater than or equal to x with the condition that the number of vertices labeled with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labeled with 0 and the number of edges labeled with 1 differ by almost 1. The graph that admits an Extended Mean Cordial Labeling is called Extended Mean Cordial Graph. In this paper, we proved that tree related graphs Hdn, K 1,n, Tgn, <K1,n:n> are Extended Mean Cordial Graphs.

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Harlander, Jens, and Stephan Rosebrock. "Aspherical word labeled oriented graphs and cyclically presented groups." Journal of Knot Theory and Its Ramifications 24, no. 05 (April 2015): 1550025. http://dx.doi.org/10.1142/s021821651550025x.

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A word labeled oriented graph (WLOG) is an oriented graph [Formula: see text] on vertices X = {x1,…,xn}, where each oriented edge is labeled by a word in X±1. WLOGs give rise to presentations which generalize Wirtinger presentations of knots. WLOG presentations, where the underlying graph is a tree, are of central importance in view of Whitehead's Asphericity Conjecture. We present a class of aspherical word labeled oriented graphs. This class can be used to produce highly non-injective aspherical labeled oriented trees and also aspherical cyclically presented groups.

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Guirao, Juan, Sarfraz Ahmad, Muhammad Siddiqui, and Muhammad Ibrahim. "Edge Irregular Reflexive Labeling for Disjoint Union of Generalized Petersen Graph." Mathematics 6, no. 12 (December 5, 2018): 304. http://dx.doi.org/10.3390/math6120304.

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A graph labeling is the task of integers, generally spoken to by whole numbers, to the edges or vertices, or both of a graph. Formally, given a graph G = ( V , E ) a vertex labeling is a capacity from V to an arrangement of integers. A graph with such a capacity characterized is known as a vertex-labeled graph. Similarly, an edge labeling is an element of E to an arrangement of labels. For this situation, the graph is called an edge-labeled graph. We examine an edge irregular reflexive k-labeling for the disjoint association of the cycle related graphs and decide the correct estimation of the reflexive edge strength for the disjoint association of s isomorphic duplicates of the cycle related graphs to be specific Generalized Peterson graphs.

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6

Matsumoto, Kengo. "C*-algebras associated with presentations of subshifts ii. ideal structure and lambda-graph subsystems." Journal of the Australian Mathematical Society 81, no. 3 (December 2006): 369–85. http://dx.doi.org/10.1017/s1446788700014373.

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AbstractA λ-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. InDoc. Math.7 (2002) 1–30, the author constructed aC*-algebraO£associated with a λ-graph system £ from a graph theoretic view-point. If a λ-graph system comes from a finite labeled graph, the algebra becomes a Cuntz-Krieger algebra. In this paper, we prove that there is a bijective correspondence between the lattice of all saturated hereditary subsets of £ and the lattice of all ideals of the algebraO£, under a certain condition on £ called (II). As a result, the class of theC*-algebras associated with λ-graph systems under condition (II) is closed under quotients by its ideals.

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7

Zhang, Zhijun, Muhammad Awais Umar, Xiaojun Ren, Basharat Rehman Ali, Mujtaba Hussain, and Xiangmei Li. "Tree-Antimagicness of Web Graphs and Their Disjoint Union." Mathematical Problems in Engineering 2020 (April 9, 2020): 1–6. http://dx.doi.org/10.1155/2020/4565829.

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In graph theory, the graph labeling is the assignment of labels (represented by integers) to edges and/or vertices of a graph. For a graph G=V,E, with vertex set V and edge set E, a function from V to a set of labels is called a vertex labeling of a graph, and the graph with such a function defined is called a vertex-labeled graph. Similarly, an edge labeling is a function of E to a set of labels, and in this case, the graph is called an edge-labeled graph. In this research article, we focused on studying super ad,d-T4,2-antimagic labeling of web graphs W2,n and isomorphic copies of their disjoint union.

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8

Bagheri Gh., Behrooz. "(G1,G2)-permutation graphs." Discrete Mathematics, Algorithms and Applications 07, no. 04 (December 2015): 1550051. http://dx.doi.org/10.1142/s1793830915500512.

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Let [Formula: see text] and [Formula: see text] be two labeled graphs of order [Formula: see text]. For any permutation [Formula: see text] the [Formula: see text]-permutation graph of labeled graphs [Formula: see text] and [Formula: see text] is the union of [Formula: see text] and [Formula: see text] together with the edges joining the vertex [Formula: see text] to the vertex [Formula: see text]. This operation on graphs is useful to produce a large class of networks with approximately the same properties as one of the original networks or even smaller. In this work we consider some properties of the permutation graph [Formula: see text], for labeled graph [Formula: see text] and [Formula: see text] of the same order. We provide bounds for the parameters radius, diameter, total distance, connectivity, edge-connectivity, chromatic number, and edge-chromatic number.

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Madhawa, Kaushalya, and Tsuyoshi Murata. "Active Learning for Node Classification: An Evaluation." Entropy 22, no. 10 (October 16, 2020): 1164. http://dx.doi.org/10.3390/e22101164.

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Current breakthroughs in the field of machine learning are fueled by the deployment of deep neural network models. Deep neural networks models are notorious for their dependence on large amounts of labeled data for training them. Active learning is being used as a solution to train classification models with less labeled instances by selecting only the most informative instances for labeling. This is especially important when the labeled data are scarce or the labeling process is expensive. In this paper, we study the application of active learning on attributed graphs. In this setting, the data instances are represented as nodes of an attributed graph. Graph neural networks achieve the current state-of-the-art classification performance on attributed graphs. The performance of graph neural networks relies on the careful tuning of their hyperparameters, usually performed using a validation set, an additional set of labeled instances. In label scarce problems, it is realistic to use all labeled instances for training the model. In this setting, we perform a fair comparison of the existing active learning algorithms proposed for graph neural networks as well as other data types such as images and text. With empirical results, we demonstrate that state-of-the-art active learning algorithms designed for other data types do not perform well on graph-structured data. We study the problem within the framework of the exploration-vs.-exploitation trade-off and propose a new count-based exploration term. With empirical evidence on multiple benchmark graphs, we highlight the importance of complementing uncertainty-based active learning models with an exploration term.

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10

JEONG, JA A., EUN JI KANG, and GI HYUN PARK. "Purely infinite labeled graph -algebras." Ergodic Theory and Dynamical Systems 39, no. 8 (December 4, 2017): 2128–58. http://dx.doi.org/10.1017/etds.2017.123.

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In this paper, we consider pure infiniteness of generalized Cuntz–Krieger algebras associated to labeled spaces $(E,{\mathcal{L}},{\mathcal{E}})$. It is shown that a $C^{\ast }$-algebra $C^{\ast }(E,{\mathcal{L}},{\mathcal{E}})$ is purely infinite in the sense that every non-zero hereditary subalgebra contains an infinite projection (we call this property (IH)) if $(E,{\mathcal{L}},{\mathcal{E}})$ is disagreeable and every vertex connects to a loop. We also prove that under the condition analogous to (K) for usual graphs, $C^{\ast }(E,{\mathcal{L}},{\mathcal{E}})=C^{\ast }(p_{A},s_{a})$ is purely infinite in the sense of Kirchberg and Rørdam if and only if every generating projection $p_{A}$, $A\in {\mathcal{E}}$, is properly infinite, and also if and only if every quotient of $C^{\ast }(E,{\mathcal{L}},{\mathcal{E}})$ has property (IH).

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11

Banjade, Debendra P., and Menassie Ephrem. "On labeled graph $C^*$-algebras." Rocky Mountain Journal of Mathematics 50, no. 3 (June 2020): 863–70. http://dx.doi.org/10.1216/rmj.2020.50.863.

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12

Sapunov, Serhii, Aleksei Senchenko, and Oleh Sereda. "Metric properties of the canonical defining pair for determined graphs." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 34 (April 24, 2021): 134–45. http://dx.doi.org/10.37069/10.37069/1683-4720-2020-34-13.

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The aim of this paper is to study the representation of deterministic graphs (D-graphs) by sets of words over the vertex labels alphabet and to find metric properties of this representation. Vertex-labeled graphs are widely used in various computational processes modeling in programming, robotics, model checking, etc. In such models graphs playing the role of an information environment of single or several mobile agents. Walks of agents on a graph determines the sequence of vertices labels or words in the alphabet of labels. A vertex-labeled graph is said to be D-graph if all vertices in the neighborhood of every its vertex have different labels. For D-graphs in case when the graph as a whole and the initial vertex (i.e. the vertex from which the agent started walking) are known there exists the one-to-one correspondence between the sequence of vertices visited by the agent and the trajectory of its walks on the graph. In case when the D-graph is not known as a whole, agent walks on it can be arranged in such way that an observer obtains information about the structure of the graph sufficient to solve the problems of graph recognizing, finding optimal path between vertices, comparison between current graph and etalon graph etc. This paper specifies the representation of D-graphs by the defining pair of sets of words (the first describes cycles of the graph and the second -- all its vertices of degree 1). This representation is an analogue of the system of defining relations for everywhere defined automata. The structure of the so-called canonical defining pair, which is minimal in terms of the number of words, is also considered. An algorithm for building such pair is developed and described in detail. For D-graphs with a given number of vertices and edges, the exact number of words in the first component of its canonical defining pair and the minimum and maximum attainable bounds for the the number of words in the second component of this pair are obtained. This representation allows us to use new methods and algorithms to solve the problems of analyzing vertex-labeled graphs.

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13

Hoogeboom, Hendrik Jan, and Grzegorz Rozenberg. "Diamond Properties of Elementary Net Systems." Fundamenta Informaticae 14, no. 3 (March 1, 1991): 287–300. http://dx.doi.org/10.3233/fi-1991-14303.

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An elementary net system is the basic system model of net theory. The state space of an elementary net system is formalized through the notion of the case graph, which is an edge-labeled graph with a distinguished initial node. The paper investigates syntactic, i.e., graph theoretic properties of case graphs of elementary net systems. In particular it studies the structure of isomorphisms between case graphs.

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14

Sun, Liang, Yuzhu Zhou, Xuan Chen, and Chuanyu Wu. "Type Synthesis and Application of Gear Linkage Transplanting Mechanisms Based on Graph Theory." Transactions of the ASABE 62, no. 2 (2019): 515–28. http://dx.doi.org/10.13031/trans.13200.

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Abstract. Type synthesis is an important step when designing innovations in mechanisms. To overcome the limitation of traditional gear train transplanting mechanisms in realizing a specific trajectory, a swinging linkage mechanism is introduced into the design of the transplanting mechanism. To design a crop-transplanting gear linkage mechanism (GLM), an automatic synthesis method based on graph theory is proposed in this article. First, the numbers of loops, links, joints and other parameters, along with unlabeled graphs, are calculated based on the structural characteristics of the GLM. The labeled graphs that correspond to the kinematic chain (KC) are then obtained by thickening the edges of the unlabeled graphs, and physically reasonable labeled graphs are derived from identification of the structural rationality of the corresponding structures. Based on the relative motion characteristics of the input and output links of the transplanting mechanisms, criteria for screening the gear linkage mechanisms represented by the labeled graphs are formulated, and the labeled graphs that are suitable for transplanting are calculated to enrich the configurations of the transplanting mechanisms. Finally, two examples are tested to verify the effectiveness of the proposed type synthesis method. Keywords: Gear linkage, Screening, Topological graph, Transplanting mechanism, Type synthesis.

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15

Sun, Ke, Zhouchen Lin, and Zhanxing Zhu. "Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labeled Nodes." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 5892–99. http://dx.doi.org/10.1609/aaai.v34i04.6048.

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Graph Convolutional Networks (GCNs) play a crucial role in graph learning tasks, however, learning graph embedding with few supervised signals is still a difficult problem. In this paper, we propose a novel training algorithm for Graph Convolutional Network, called Multi-Stage Self-Supervised (M3S) Training Algorithm, combined with self-supervised learning approach, focusing on improving the generalization performance of GCNs on graphs with few labeled nodes. Firstly, a Multi-Stage Training Framework is provided as the basis of M3S training method. Then we leverage DeepCluster technique, a popular form of self-supervised learning, and design corresponding aligning mechanism on the embedding space to refine the Multi-Stage Training Framework, resulting in M3S Training Algorithm. Finally, extensive experimental results verify the superior performance of our algorithm on graphs with few labeled nodes under different label rates compared with other state-of-the-art approaches.

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Bača, Martin, Nurdin Hinding, Aisha Javed, and Andrea Semaničová-Feňovčíková. "H-Irregularity Strengths of Plane Graphs." Symmetry 13, no. 2 (January 30, 2021): 229. http://dx.doi.org/10.3390/sym13020229.

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Graph labeling is the mapping of elements of a graph (which can be vertices, edges, faces or a combination) to a set of numbers. The mapping usually produces partial sums (weights) of the labeled elements of the graph, and they often have an asymmetrical distribution. In this paper, we study vertex–face and edge–face labelings of two-connected plane graphs. We introduce two new graph characteristics, namely the vertex–face H-irregularity strength and edge–face H-irregularity strength of plane graphs. Estimations of these characteristics are obtained, and exact values for two families of graphs are determined.

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Jeyanthi, P., and D. Ramya. "On Construction of Mean Graphs." Journal of Scientific Research 5, no. 2 (April 22, 2013): 265–73. http://dx.doi.org/10.3329/jsr.v5i2.11545.

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A graph with p vertices and q edges is called a mean graph if there is an injective function f that maps V(G) to such that for each edge uv, is labeled with if is even and if is odd. Then the resulting edge labels are distinct. In this paper, we prove some general theorems on mean graphs and show that the graphs , Jewel graph , Jelly fish graph and are mean graphs.Keywords: Mean labeling; Mean graph.© 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v5i2.11545 J. Sci. Res. 5 (2), 265-273 (2013)

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Moon, Heekyung, Zhanfang Zhao, Jintak Choi, and Sungkook Han. "A novel property graph model for knowledge representation on the Web." International Journal of Engineering & Technology 7, no. 3.33 (August 29, 2018): 187. http://dx.doi.org/10.14419/ijet.v7i3.33.21010.

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Graphs provide an effective way to represent information and knowledge of real world domains. Resource Description Framework (RDF) model and Labeled Property Graphs (LPG) model are dominant graph data models widely used in Linked Open Data (LOD) and NoSQL databases. Although these graph models have plentiful data modeling capabilities, they reveal some drawbacks to model the complicated structures. This paper proposes a new property graph model called a universal property graph (UPG) that can embrace the capability of both RDF and LPG. This paper explores the core features of UPG and their functions.

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19

Burlyaeva, E. V., V. V. Burlyaev, and V. S. Tsekhanovich. "SET-THEORETIC DESCRITPION OF FUNCTIONAL MODELS OF CHEMICAL MANUFACTURING." Fine Chemical Technologies 12, no. 5 (October 28, 2017): 71–78. http://dx.doi.org/10.32362/2410-6593-2017-12-5-71-78.

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The technique for the formalized description of functional models of chemical manufacturing is developed. The technique is based on graph theory. The model is described as a set of oriented labeled graphs that are hierarchically organized by the decompose relationship. First we describe the conversion of a single diagram to a labeled graph, including adding new nodes and edges. The nodes of the graph correspond to boxes, borders and branching points of the arrows at the diagram. The edges of the graph correspond to the arrows at the diagram. The graph descriptions of the model of base functional relationships such as output-input, output-control, output-mechanism are represented. We develop procedures to convert the border arrows and branch arrows. Conversion of branch arrows is performed depending on changes of the labels of branches. Branching of each arrow corresponds to a subgraph including several edges and perhaps additional nodes. Oriented labeled graphs are described by set-theoretic notation that contains the labels of the edges and the roles of nodes. The hierarchy of diagrams is specified by a decompose relationship, which includes the parent chart, the child chart and the decomposed box. As an example, we present the set-theoretic description of the functional model of vinyl acetate manufacturing. The application of mathematical apparatus built within the framework of graph theory for verification and analysis of functional diagrams based on the proposed formal description is an area for further research.

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Jassim, W. S. "Incidence Matrices of X-Labled Graphs and an Application." Sultan Qaboos University Journal for Science [SQUJS] 14 (June 1, 2009): 61. http://dx.doi.org/10.24200/squjs.vol14iss0pp61-69.

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In this work, we have made some modifications on the definition of the incidence matrices of a directed graph, to let the incidence matrices to be more confident for X – Labeled graphs. The new incidence matrices are called the incidence matrices of X – Labeled graphs, and we used the new definition to give a computer program for Nickolas`s Algorithm .

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Zhao, Ruiqi, and Aleix M. Martinez. "Labeled Graph Kernel for Behavior Analysis." IEEE Transactions on Pattern Analysis and Machine Intelligence 38, no. 8 (August 1, 2016): 1640–50. http://dx.doi.org/10.1109/tpami.2015.2481404.

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22

Ullmann, Julian R. "Degree Reduction in Labeled Graph Retrieval." ACM Journal of Experimental Algorithmics 20 (December 15, 2015): 1–54. http://dx.doi.org/10.1145/2699878.

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23

von der Malsburg, Christoph. "Pattern recognition by labeled graph matching." Neural Networks 1, no. 2 (January 1988): 141–48. http://dx.doi.org/10.1016/0893-6080(88)90016-0.

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24

Vaidya, S. K., and N. H. Shah. "Some New Results on Prime Cordial Labeling." ISRN Combinatorics 2014 (March 23, 2014): 1–9. http://dx.doi.org/10.1155/2014/607018.

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A prime cordial labeling of a graph G with the vertex set V(G) is a bijection f:V(G)→{1,2,3,…,|V(G)|} such that each edge uv is assigned the label 1 if gcd(f(u),f(v))=1 and 0 if gcd(f(u),f(v))>1; then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph which admits a prime cordial labeling is called a prime cordial graph. In this work we give a method to construct larger prime cordial graph using a given prime cordial graph G. In addition to this we have investigated the prime cordial labeling for double fan and degree splitting graphs of path as well as bistar. Moreover we prove that the graph obtained by duplication of an edge (spoke as well as rim) in wheel Wn admits prime cordial labeling.

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Song, Chunyao, Tingjian Ge, Yao Ge, Haowen Zhang, and Xiaojie Yuan. "Labeled graph sketches: Keeping up with real-time graph streams." Information Sciences 503 (November 2019): 469–92. http://dx.doi.org/10.1016/j.ins.2019.07.019.

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Wamiliana, Wamiliana, Amanto Amanto, Mustofa Usman, Muslim Ansori, and Fadila Cahya Puri. "Enumerating the Number of Connected Vertices Labeled Graph of Order Six with Maximum Ten Loops and Containing No Parallel Edges." Science and Technology Indonesia 5, no. 4 (October 9, 2020): 131. http://dx.doi.org/10.26554/sti.2020.5.4.131-135.

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A Graph G (V, E) is said to be a connected graph if for every two vertices on the graph there exist at least a path connecting them, otherwise, the graph is disconnected. Two edges or more that connect the same pair of vertices are called parallel edges, and an edge that starts and ends at the same vertex is called a loop. A graph is called simple if it containing no loops nor parallel edges. Given n vertices and m edges, m ≥ 1, there are many graphs that can be formed, either connected or disconnected. In this research, we will discuss how to calculate the number of connected vertices labeled graphs of order six (isomorphism graphs are counted as one), with a maximum loop of ten without parallel edges.

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Zhang, H., J. J. Zhou, and R. Li. "Enhanced Unsupervised Graph Embedding via Hierarchical Graph Convolution Network." Mathematical Problems in Engineering 2020 (July 26, 2020): 1–9. http://dx.doi.org/10.1155/2020/5702519.

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Graph embedding aims to learn the low-dimensional representation of nodes in the network, which has been paid more and more attention in many graph-based tasks recently. Graph Convolution Network (GCN) is a typical deep semisupervised graph embedding model, which can acquire node representation from the complex network. However, GCN usually needs to use a lot of labeled data and additional expressive features in the graph embedding learning process, so the model cannot be effectively applied to undirected graphs with only network structure information. In this paper, we propose a novel unsupervised graph embedding method via hierarchical graph convolution network (HGCN). Firstly, HGCN builds the initial node embedding and pseudo-labels for the undirected graphs, and then further uses GCNs to learn the node embedding and update labels, finally combines HGCN output representation with the initial embedding to get the graph embedding. Furthermore, we improve the model to match the different undirected networks according to the number of network node label types. Comprehensive experiments demonstrate that our proposed HGCN and HGCN∗ can significantly enhance the performance of the node classification task.

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Koam, Ali N. A., Muhammad Akram, and Peide Liu. "Decision-Making Analysis Based on Fuzzy Graph Structures." Mathematical Problems in Engineering 2020 (August 12, 2020): 1–30. http://dx.doi.org/10.1155/2020/6846257.

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A graph structure is a useful framework to solve the combinatorial problems in various fields of computational intelligence systems and computer science. In this research article, the concept of fuzzy sets is applied to the graph structure to define certain notions of fuzzy graph structures. Fuzzy graph structures can be very useful in the study of various structures, including fuzzy graphs, signed graphs, and the graphs having labeled or colored edges. The notions of the fuzzy graph structure, lexicographic-max product, and degree and total degree of a vertex in the lexicographic-max product are introduced. Further, the proposed concepts are explained through several numerical examples. In particular, applications of the fuzzy graph structures in decision-making process, regarding detection of marine crimes and detection of the road crimes, are presented. Finally, the general procedure of these applications is described by an algorithm.

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Jeong, Ja A., and Gi Hyun Park. "Simple labeled graph C⁎-algebras are associated to disagreeable labeled spaces." Journal of Mathematical Analysis and Applications 461, no. 2 (May 2018): 1391–403. http://dx.doi.org/10.1016/j.jmaa.2018.01.045.

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Shan, Xiaohuan, Haihai Li, Chunjie Jia, Dong Li, and Baoyan Song. "Supergraph Topology Feature Index for Personalized Interesting Subgraph Query in Large Labeled Graphs." Complexity 2021 (June 29, 2021): 1–18. http://dx.doi.org/10.1155/2021/9274429.

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Interesting subgraph query aims to find subgraphs that are isomorphic to the given query graph from a data graph and rank the subgraphs according to their interestingness scores. However, the existing subgraph query approaches are inefficient when dealing with large-scale labeled data graph. This is caused by the following problems: (i) the existing work mainly focuses on unweighted query graphs, while ignoring the impact of query constraints on query results. (ii) Excessive number of subgraph candidates or complex joins between nodes in the subgraph candidates reduce the query efficiency. To solve these problems, this paper proposes an intelligent solution. Firstly, an Isotype Structure Graph Compression (ISGC) strategy is proposed to compress similar nodes in a graph to reduce the size of the graph and avoid unnecessary matching. Then, an auxiliary data structure Supergraph Topology Feature Index (STFIndex) is designed to replace the storage of the original data graph and improve the efficiency of an online query. After that, a partition method based on Edge Label Step Value (ELSV) is proposed to partition the index logically. In addition, a novel Top-K interest subgraph query approach is proposed, which consists of the multidimensional filtering (MDF) strategy, upper bound value (UBV) (Size-c) matching, and the optimizational join (QJ) method to filter out as many false subgraph candidates as possible to achieve fast joins. We conduct experiments on real and synthetic datasets. Experimental results show that the average performance of our approach is 1.35 higher than that of the state-of-the-art approaches when the query graph is unweighted, and the average performance of our approach is 2.88 higher than that of the state-of-the-art approaches when the query graph is weighted.

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White, Arthur T. "An Introduction to Random Topological Graph Theory." Combinatorics, Probability and Computing 3, no. 4 (December 1994): 545–55. http://dx.doi.org/10.1017/s0963548300001395.

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We introduce five probability models for random topological graph theory. For two of these models (I and II), the sample space consists of all labeled orientable 2-cell imbeddings of a fixed connected graph, and the interest centers upon the genus random variable. Exact results are presented for the expected value of this random variable for small-order complete graphs, for closed-end ladders, and for cobblestone paths. The expected genus of the complete graph is asymptotic to the maximum genus. For Model III, the sample space consists of all labeled 2-cell imbeddings (possibly nonorientable) of a fixed connected graph, and for Model IV the sample space consists of all such imbeddings with a rotation scheme also fixed. The event of interest is that the ambient surface is orientable. In both these models the complete graph is almost never orientably imbedded. The probability distribution in Models I and III is uniform; in Models II and IV it depends on a parameter p and is uniform precisely when p = 1/2. Model V combines the features of Models II and IV.

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Jiang, Huiqin, Pu Wu, Zehui Shao, Yongsheng Rao, and Jia-Bao Liu. "The Double Roman Domination Numbers of Generalized Petersen Graphs P(n, 2)." Mathematics 6, no. 10 (October 16, 2018): 206. http://dx.doi.org/10.3390/math6100206.

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A double Roman dominating function (DRDF) f on a given graph G is a mapping from V ( G ) to { 0 , 1 , 2 , 3 } in such a way that a vertex u for which f ( u ) = 0 has at least a neighbor labeled 3 or two neighbors both labeled 2 and a vertex u for which f ( u ) = 1 has at least a neighbor labeled 2 or 3. The weight of a DRDF f is the value w ( f ) = ∑ u ∈ V ( G ) f ( u ) . The minimum weight of a DRDF on a graph G is called the double Roman domination number γ d R ( G ) of G. In this paper, we determine the exact value of the double Roman domination number of the generalized Petersen graphs P ( n , 2 ) by using a discharging approach.

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Akutsu, Tatsuya, Avraham A. Melkman, and Takeyuki Tamura. "Improved Hardness of Maximum Common Subgraph Problems on Labeled Graphs of Bounded Treewidth and Bounded Degree." International Journal of Foundations of Computer Science 31, no. 02 (February 2020): 253–73. http://dx.doi.org/10.1142/s0129054120500069.

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We consider the maximum common connected edge subgraph problem and the maximum common connected induced subgraph problem for simple graphs with labeled vertices (or labeled edges). The former is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs. The latter is to find a common connected induced subgraph with the maximum number of vertices. We prove that both problems are NP-hard for 3-outerplanar labeled graphs even if the maximum vertex degree is bounded by 4. Since the reductions used in the proofs construct graphs with treewidth at most 4, both problems are NP-hard also for such graphs, which significantly improves the previous hardness results for graphs with treewidth 11. We also present improved exponential-time algorithms for both problems on labeled graphs of bounded treewidth and bounded vertex degree.

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Siehler, Jacob A. "Xor-Magic Graphs." Recreational Mathematics Magazine 6, no. 11 (September 1, 2019): 35–44. http://dx.doi.org/10.2478/rmm-2019-0004.

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Abstract A connected graph on 2n vertices is defined to be xor-magic if the vertices can be labeled with distinct n-bit binary numbers in such a way that the label at each vertex is equal to the bitwise xor of the labels on the adjacent vertices. We show that there is at least one 3-regular xor-magic graph on 2n vertices for every n ⩾ 2. We classify the 3-regular xor-magic graphs on 8 and 16 vertices, and give multiple examples of 3-regular xor-magic graphs on 32 vertices, including the well-known Dyck graph.

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35

Tsvetov, V. P. "ON A SUPERCLASS OF A-GRAMMARS." Vestnik of Samara University. Natural Science Series 20, no. 10 (May 29, 2017): 102–8. http://dx.doi.org/10.18287/2541-7525-2014-20-10-102-108.

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In this paper we consider a superclass of automaton grammars that can be represented in terms of paths on graphs. With this approach, we assume that vertices of graph are labeled by symbols of ﬁnite alphabet A . We will call such grammars graph-generated grammars or G-grammars. In contrast to the graph grammars that are used to describe graph structure transformations, G-grammars using a graphs as a means of representing formal languages. We will give an algorithm for constructing G-grammar which generate the language recognized by deterministic ﬁnite automaton. Moreover, we will show that the class of languages generated by G-grammars is a proper superset of regular languages.

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36

Sapunov, Sergey Valerievich. "Reconstruction of a Labeled Graph by a Graph-walking Mobile Agent." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 15, no. 2 (June 2015): 228–38. http://dx.doi.org/10.18500/1816-9791-2015-15-2-228-238.

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Matsumoto, Kengo. "Construction and pure infiniteness of $C^*$-algebras associated with lambda-graph systems." MATHEMATICA SCANDINAVICA 97, no. 1 (September 1, 2005): 73. http://dx.doi.org/10.7146/math.scand.a-14964.

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A $\lambda$-graph system is a labeled Bratteli diagram with shift transformation. It is a generalization of finite labeled graphs and presents a subshift. In [16] the author has introduced a $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ associated with a $\lambda$-graph system $\mathfrak{L}$ by using groupoid method as a generalization of the Cuntz-Krieger algebras. In this paper, we concretely construct the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ by using both creation operators and projections on a sub Fock Hilbert space associated with $\mathfrak{L}$. We also introduce a new irreducible condition on $\mathfrak{L}$ under which the $C^*$-algebra $\mathcal{O}_{\mathfrak{L}}$ becomes simple and purely infinite.

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38

Aigner, Martin, and Eberhard Triesch. "Reconstructing a Graph from its Neighborhood Lists." Combinatorics, Probability and Computing 2, no. 2 (June 1993): 103–13. http://dx.doi.org/10.1017/s0963548300000535.

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Associate to a finite labeled graph G(V, E) its multiset of neighborhoods (G) = {N(υ): υ ∈ V}. We discuss the question of when a list is realizable by a graph, and to what extent G is determined by (G). The main results are: the decision problem is NP-complete; for bipartite graphs the decision problem is polynomially equivalent to Graph Isomorphism; forests G are determined up to isomorphism by (G); and if G is connected bipartite and (H) = (G), then H is completely described.

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Palanikumar, R., and A. Rameshkumar. "Wiener index of physio-chemical labeled graph." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 37e, no. 2 (2018): 519. http://dx.doi.org/10.5958/2320-3226.2018.00056.5.

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Bhat, Pradeep G., and Sabitha D'Souza. "Minimum Covering Energy of Binary Labeled Graph." International Journal of Mathematics and Soft Computing 4, no. 2 (July 13, 2014): 153. http://dx.doi.org/10.26708/ijmsc.2014.2.4.16.

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Hassin, Refael, Jérôme Monnot, and Danny Segev. "The Complexity of Bottleneck Labeled Graph Problems." Algorithmica 58, no. 2 (December 17, 2008): 245–62. http://dx.doi.org/10.1007/s00453-008-9261-4.

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Nishimura, Naomi, Prabhakar Ragde, and Dimitrios M. Thilikos. "On Graph Powers for Leaf-Labeled Trees." Journal of Algorithms 42, no. 1 (January 2002): 69–108. http://dx.doi.org/10.1006/jagm.2001.1195.

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43

Dănciulescu, Dana, and Mihaela Colhon. "Splitting the structured paths in stratified graphs. Application in Natural Language Generation." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 2 (June 1, 2014): 57–68. http://dx.doi.org/10.2478/auom-2014-0031.

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AbstractThe concept of labeled stratified graph (LSG) introduces some method of knowledge representation. The inference process developed for this structures uses the paths of the stratified graphs, an order between the elementary arcs of a path and some results of universal algebras. The order is defined by considering a structured path instead of a regular path. The application described in this paper interprets the symbolic elements of a LSG with natural language constructions. In this manner we obtained a mechanism for generation coherent texts in a natural language (for this approach, Romanian). The generation method is based on labeled stratified graph representation and the inference mechanism is guided by the structured paths of these representations.

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Jamshidpour, N., S. Homayouni, and A. Safari. "GRAPH-BASED SEMI-SUPERVISED HYPERSPECTRAL IMAGE CLASSIFICATION USING SPATIAL INFORMATION." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W4 (September 26, 2017): 91–96. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w4-91-2017.

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Hyperspectral image classification has been one of the most popular research areas in the remote sensing community in the past decades. However, there are still some problems that need specific attentions. For example, the lack of enough labeled samples and the high dimensionality problem are two most important issues which degrade the performance of supervised classification dramatically. The main idea of semi-supervised learning is to overcome these issues by the contribution of unlabeled samples, which are available in an enormous amount. In this paper, we propose a graph-based semi-supervised classification method, which uses both spectral and spatial information for hyperspectral image classification. More specifically, two graphs were designed and constructed in order to exploit the relationship among pixels in spectral and spatial spaces respectively. Then, the Laplacians of both graphs were merged to form a weighted joint graph. The experiments were carried out on two different benchmark hyperspectral data sets. The proposed method performed significantly better than the well-known supervised classification methods, such as SVM. The assessments consisted of both accuracy and homogeneity analyses of the produced classification maps. The proposed spectral-spatial SSL method considerably increased the classification accuracy when the labeled training data set is too scarce.When there were only five labeled samples for each class, the performance improved 5.92% and 10.76% compared to spatial graph-based SSL, for AVIRIS Indian Pine and Pavia University data sets respectively.

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45

Kozak, Marcin. "Displaying Labeled Quantitative Data." Social Communication 5, no. 2 (December 1, 2019): 11–20. http://dx.doi.org/10.2478/sc-2019-0005.

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Abstract The information world is full of labeled quantitative data, in which a number of qualitative categories are to be compared based on a quantitative variable. Their graphical representations are various and serve different audiences and purposes. Based on a simple data set and its different visualizations, we will play with the data and their visual representation. We will use well-known charts, such as a regular table, a bar plot, and a word cloud; less-know, such as Cleveland’s dot plot, a fan plot, and a text-table; and new ones, constructed for the very aim of this essay, such as a labeled rectangle plot and a ruler-like graph. Our discussion will not aim to choose the best graph but rather to show the different faces of visualizing labeled quantitative data. I hope to convince the readers that it is always worth spending a minute on pondering how to present their data.

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Youssef, Maged Zakaria, and Zainab Saad Almoreed. "On odd prime labeling of graphs." Open Journal of Discrete Applied Mathematics 3, no. 3 (October 20, 2020): 33–40. http://dx.doi.org/10.30538/psrp-odam2020.0041.

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In this paper we give a new variation of the prime labeling. We call a graph \(G\) with vertex set \(V(G)\) has an odd prime labeling if its vertices can be labeled distinctly from the set \(\big\{1, 3, 5, ...,2\big|V(G)\big| -1\big\}\) such that for every edge \(xy\) of \(E(G)\) the labels assigned to the vertices of \(x\) and \(y\) are relatively prime. A graph that admits an odd prime labeling is called an <i>odd prime graph</i>. We give some families of odd prime graphs and give some necessary conditions for a graph to be odd prime. Finally, we conjecture that every prime graph is odd prime graph.

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Kheibari, M., H. Abdollahzadeh Ahangar, R. Khoeilar, and S. M. Sheikholeslami. "Total Roman 2 -Reinforcement of Graphs." Journal of Mathematics 2021 (April 10, 2021): 1–7. http://dx.doi.org/10.1155/2021/5515250.

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A total Roman 2 -dominating function (TR2DF) on a graph Γ = V , E is a function l : V ⟶ 0,1,2 , satisfying the conditions that (i) for every vertex y ∈ V with l y = 0 , either y is adjacent to a vertex labeled 2 under l , or y is adjacent to at least two vertices labeled 1; (ii) the subgraph induced by the set of vertices with positive weight has no isolated vertex. The weight of a TR2DF l is the value ∑ y ∈ V l y . The total Roman 2 -domination number (TR2D-number) of a graph Γ is the minimum weight of a TR2DF on Γ . The total Roman 2 -reinforcement number (TR2R-number) of a graph is the minimum number of edges that have to be added to the graph in order to decrease the TR2D-number. In this manuscript, we study the properties of TR2R-number and we present some sharp upper bounds. In particular, we determine the exact value of TR2R-numbers of some classes of graphs.

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48

Nurhakim, Rusdan. "An Odd-Even Sum Labeling of Jellyfish and Mushroom Graphs." InPrime: Indonesian Journal of Pure and Applied Mathematics 2, no. 2 (June 7, 2020): 87–90. http://dx.doi.org/10.15408/inprime.v2i2.14620.

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AbstractA graph G(V,E) with p vertices and q edges called graph odd-even sum if there exists an injective function f from V to {+ 1, +2, +3, ..., +(2p-1)} such that induced a bijection f*(uv)=f(u)+f(v) as label of edge and u,v element of V forms the set {2,4,...,2q}, and f is called odd-even sum labeling. There are three criteria of graphs that can be labeled by this labeling, they are undirected, no loops, and finite for every edges and vertex. Jellyfish J(m,n) graph and Mushroom Mr(m) graph have the criteria. So in this paper will be showed that the Jellyfish and Mushroom graphs can be labeled by this labeling.Keywords: odd-even sum graph; odd-even sum labeling; Jellyfish and mushroom graphs. AbstrakGraf G(V,E) dengan banyak titik p dan sisi q dikatakan graf jumlah ganjil-genap jika terdapat suatu fungsi injetif f dari V ke {+ 1, +2, +3, ..., +(2p-1)} sehingga bijektif f*(uv)=f(u)+f(v) merupakan label sisi dengan u,v anggota dari V membentuk himpunan bilangan {2,4,...,2q}, dengan f merupakan pelabelan jumlah ganjil-genap. Kriteria graf yang dapat dilabeli oleh pelabelan jumlah ganjil-genap ada tiga, yaitu graf yang tidak berarah, tidak memiliki loop, dan terhingga, baik secara sisi maupun titik. Graf Jellyfish J(m,n) dan Mushroom Mr(m) memenuhi ketiga kriteria tersebut. Pada tulisan ini akan ditunjukkan bahwa kedua graf tersebut dapat dilabeli dengan pelabelan jumlah ganjil-genap.Keywords: graf jumlah ganjil-genap; pelabelan jumlah ganjil-genap; graf Jellyfish dan graf Mushroom.

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Yao, Huaxiu, Chuxu Zhang, Ying Wei, Meng Jiang, Suhang Wang, Junzhou Huang, Nitesh Chawla, and Zhenhui Li. "Graph Few-Shot Learning via Knowledge Transfer." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 6656–63. http://dx.doi.org/10.1609/aaai.v34i04.6142.

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Towards the challenging problem of semi-supervised node classification, there have been extensive studies. As a frontier, Graph Neural Networks (GNNs) have aroused great interest recently, which update the representation of each node by aggregating information of its neighbors. However, most GNNs have shallow layers with a limited receptive field and may not achieve satisfactory performance especially when the number of labeled nodes is quite small. To address this challenge, we innovatively propose a graph few-shot learning (GFL) algorithm that incorporates prior knowledge learned from auxiliary graphs to improve classification accuracy on the target graph. Specifically, a transferable metric space characterized by a node embedding and a graph-specific prototype embedding function is shared between auxiliary graphs and the target, facilitating the transfer of structural knowledge. Extensive experiments and ablation studies on four real-world graph datasets demonstrate the effectiveness of our proposed model and the contribution of each component.

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50

Ahmad, Yasir, Umer Ali, Muhammad bilal, Sohail Zafar, and Zohaib Zahid. "Some new standard graphs labeled by 3–total edge product cordial labeling." Applied Mathematics and Nonlinear Sciences 2, no. 1 (February 17, 2017): 61–72. http://dx.doi.org/10.21042/amns.2017.1.00005.

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AbstractIn this paper, we study 3–total edge product cordial (3–TEPC) labeling which is a variant of edge product cordial labeling. We discuss Web, Helm, Ladder and Gear graphs in this context of 3–TEPC labeling. We also discuss 3–TEPC labeling of some particular examples with corona graph.

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