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Journal articles on the topic 'Graph'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

CSIKVÁRI, PÉTER, and ZOLTÁN LÓRÁNT NAGY. "The Density Turán Problem." Combinatorics, Probability and Computing 21, no. 4 (2012): 531–53. http://dx.doi.org/10.1017/s0963548312000016.

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LetHbe a graph onnvertices and let the blow-up graphG[H] be defined as follows. We replace each vertexviofHby a clusterAiand connect some pairs of vertices ofAiandAjif (vi,vj) is an edge of the graphH. As usual, we define the edge density betweenAiandAjasWe study the following problem. Given densities γijfor each edge (i,j) ∈E(H), one has to decide whether there exists a blow-up graphG[H], with edge densities at least γij, such that one cannot choose a vertex from each cluster, so that the obtained graph is isomorphic toH,i.e., noHappears as a transversal inG[H]. We calldcrit(H) the maximal va

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Cappelletti, Luca, Tommaso Fontana, Elena Casiraghi, et al. "GRAPE for fast and scalable graph processing and random-walk-based embedding." Nature Computational Science 3, no. 6 (2023): 552–68. http://dx.doi.org/10.1038/s43588-023-00465-8.

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AbstractGraph representation learning methods opened new avenues for addressing complex, real-world problems represented by graphs. However, many graphs used in these applications comprise millions of nodes and billions of edges and are beyond the capabilities of current methods and software implementations. We present GRAPE (Graph Representation Learning, Prediction and Evaluation), a software resource for graph processing and embedding that is able to scale with big graphs by using specialized and smart data structures, algorithms, and a fast parallel implementation of random-walk-based meth

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Liu, Yu, and Lihua You. "Further Results on the Nullity of Signed Graphs." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/483735.

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The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we apply the coefficient theorem on the characteristic polynomial of a signed graph and give two formulae on the nullity of signed graphs with cut-points. As applications of the above results, we investigate the nullity of the bicyclic signed graphΓ∞p,q,l, obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.

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Ji, Shengwei, Chenyang Bu, Lei Li, and Xindong Wu. "Local Graph Edge Partitioning." ACM Transactions on Intelligent Systems and Technology 12, no. 5 (2021): 1–25. http://dx.doi.org/10.1145/3466685.

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Graph edge partitioning, which is essential for the efficiency of distributed graph computation systems, divides a graph into several balanced partitions within a given size to minimize the number of vertices to be cut. Existing graph partitioning models can be classified into two categories: offline and streaming graph partitioning models. The former requires global graph information during the partitioning, which is expensive in terms of time and memory for large-scale graphs. The latter creates partitions based solely on the received graph information. However, the streaming model may resul

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Kok, Johan. "Note: Certain bounds in respect of upper deg-centric graphs." Open Journal of Discrete Applied Mathematics 7, no. 2 (2024): 1–6. https://doi.org/10.30538/psrp-odam2024.0097.

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This note presents some upper bounds for the size of the upper deg-centric grapg \(G_{ud}\) of a simple connected graph G. Amongst others, a result for graphs for which a compliant graph \(G\) has \(G_{ud} \cong \overline G\) is presented. Finally, results for size minimality in respect upper deg-centrication and minimum size of such graph \(G\) are presented.

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Duan, Yucong, Lixu Shao, and Gongzhu Hu. "Specifying Knowledge Graph with Data Graph, Information Graph, Knowledge Graph, and Wisdom Graph." International Journal of Software Innovation 6, no. 2 (2018): 10–25. http://dx.doi.org/10.4018/ijsi.2018040102.

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Knowledge graphs have been widely adopted, in large part owing to their schema-less nature. It enables knowledge graphs to grow seamlessly and allows for new relationships and entities as needed. A knowledge graph is a graph constructed by representing each item, entity and user as nodes, and linking those nodes that interact with each other via edges. Knowledge graphs have abundant natural semantics and can contain various and more complete information. It is an expression mechanism close to natural language. However, we still lack a unified definition and standard expression form of knowledg

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Sohn, Moo Young, and Jaeun Lee. "Characteristic polynomials of some weighted graph bundles and its application to links." International Journal of Mathematics and Mathematical Sciences 17, no. 3 (1994): 503–10. http://dx.doi.org/10.1155/s0161171294000748.

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In this paper, we introduce weighted graph bundles and study their characteristic polynomial. In particular, we show that the characteristic polynomial of a weightedK2(K¯2)-bundles over a weighted graphG?can be expressed as a product of characteristic polynomials two weighted graphs whose underlying graphs areGAs an application, we compute the signature of a link whose corresponding weighted graph is a double covering of that of a given link.

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JOHANNSEN, DANIEL, MICHAEL KRIVELEVICH, and WOJCIECH SAMOTIJ. "Expanders Are Universal for the Class of All Spanning Trees." Combinatorics, Probability and Computing 22, no. 2 (2013): 253–81. http://dx.doi.org/10.1017/s0963548312000533.

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A graph is calleduniversalfor a given graph class(or, equivalently,-universal) if it contains a copy of every graph inas a subgraph. The construction of sparse universal graphs for various classeshas received a considerable amount of attention. There is particular interest in tight-universal graphs, that is, graphs whose number of vertices is equal to the largest number of vertices in a graph from. Arguably, the most studied case is that whenis some class of trees. In this work, we are interested in(n,Δ), the class of alln-vertex trees with maximum degree at most Δ. We show that everyn-vertex

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9

Kaviya, S., G. Mahadevan, and C. Sivagnanam. "Generalizing TCCD-Number For Power Graph Of Some Graphs." Indian Journal Of Science And Technology 17, SPI1 (2024): 115–23. http://dx.doi.org/10.17485/ijst/v17sp1.243.

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Objective: Finding the triple connected certified domination number for the power graph of some peculiar graphs. Methods: A dominating set with the condition that every vertex in has either zero or at least two neighbors in and is triple connected is a called triple connected certified domination number of a graph. The minimum cardinality among all the triple connected certified dominating sets is called the triple connected certified domination number and is denoted by . The upper bound and lower bound of for the given graphs is found and then proved the upper bound and lower bound of were eq

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10

Simonet, Geneviève, and Anne Berry. "Properties and Recognition of Atom Graphs." Algorithms 15, no. 8 (2022): 294. http://dx.doi.org/10.3390/a15080294.

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The atom graph of a connected graph is a graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all its atom trees. A graph G is an atom graph if there is a graph whose atom graph is isomorphic to G. We study the class of atom graphs, which is also the class of atom graphs of chordal graphs, and the associated recognition problem. We prove that each atom graph is a perfect graph and give a characterization of atom graphs in terms of a spanning tree, inspired by the characterization of clique graphs of chordal graphs

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11

Wafiq, Hibi. "Non-Isomorphism Between Graph And Its Complement." Multicultural Education 7, no. 6 (2021): 256. https://doi.org/10.5281/zenodo.4965942.

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<em>It is known that any graph with six vertices cannot be isomorphic to its complement [3].V. K. Balakrishnan has written in his book Schaum’s solved problems series [1] the following: “Given two arbitrary Simple graphs of the same order and the same size, the problem of determining whetheran isomorphism exists between the two is known as the isomorphism problem in graph theory. In general, itis not all easy (in other words, there is no "efficient algorithm") to solve an arbitrary instance of the isomorphismproblem”, from here came the idea of this paper. As mentio

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Basavanagoud, B., and Roopa S. Kusugal. "On the Line Degree Splitting Graph of a Graph." Bulletin of Mathematical Sciences and Applications 18 (May 2017): 1–10. http://dx.doi.org/10.18052/www.scipress.com/bmsa.18.1.

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In this paper, we introduce the concept of the line degree splitting graph of a graph. We obtain some properties of this graph. We find the girth of the line degree splitting graphs. Further, we establish the characterization of graphs whose line degree splitting graphs are eulerian, complete bipartite graphs and complete graphs.

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Demirci, Musa, Sadik Delen, Ahmet Sinan Cevik, and Ismail Naci Cangul. "Omega Index of Line and Total Graphs." Journal of Mathematics 2021 (September 27, 2021): 1–6. http://dx.doi.org/10.1155/2021/5552202.

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A derived graph is a graph obtained from a given graph according to some predetermined rules. Two of the most frequently used derived graphs are the line graph and the total graph. Calculating some properties of a derived graph helps to calculate the same properties of the original graph. For this reason, the relations between a graph and its derived graphs are always welcomed. A recently introduced graph index which also acts as a graph invariant called omega is used to obtain such relations for line and total graphs. As an illustrative exercise, omega values and the number of faces of the li

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Bursal, Murat, and Serap Yetiş. "Middle School Students’ Graph Skills and Affective States about Graphs." International Journal of Research in Education and Science 6, no. 4 (2020): 692. http://dx.doi.org/10.46328/ijres.v6i4.1136.

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This survey design study was designed to test whether the graph skills and affective states of middle school students about graphs differ by their gender, grade level, and graph types (line, bar, and pie). The data collection instruments consisted of two scales developed by the authors and a Graph Skills Test, which consisted of graph questions from the previous TIMSS and PISA exams. Based on the findings, while middle school students were found to succeed at reading the data level graph questions, they were found to struggle in questions requiring higher graph skills, such as graph interpreta

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Lakshmanan S., Aparna, S. B. Rao, and A. Vijayakumar. "Gallai and anti-Gallai graphs of a graph." Mathematica Bohemica 132, no. 1 (2007): 43–54. http://dx.doi.org/10.21136/mb.2007.133996.

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Radha, K., and A. Jasmine Kingsly. "Cardinality and Isomorphic Properties of Hajós Graphs and Hajós Fuzzy Graphs." Indian Journal Of Science And Technology 17, no. 37 (2024): 3871–80. http://dx.doi.org/10.17485/ijst/v17i37.2492.

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Objectives: Fuzzy graphs allow uncertainty in the ideas characterizing vertices and edges to be included when modelling real-world scenarios into graph models. This study aims to introduce Hajós fuzzy graph, cardinality of Hajós graph and Hajós fuzzy graph and to explore many properties. Methods : Here, the Hajós construction is applied to two fuzzy graphs, and the Hajós fuzzy graph is defined by assigning membership values to all the edges and vertices of the newly formed fuzzy graph. Fuzzy graph conditions are verified for the assigned membership values. Examples are used to illustrate the c

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17

S, Balakrishnan, Mohamed Ali A, and Rama Murthi K. "A Study on Different types of Product of Anti Fuzzy Graphs." Journal of Computational Mathematica 7, no. 1 (2023): 131–38. http://dx.doi.org/10.26524/cm168.

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In this article, we consider to obtain new anti fuzzy graph from given anti fuzzy graphs. Product of anti fuzzy graphs is an operation on anti fuzzy graphs that produce new anti fuzzy graph. We consider tensor, normal, modular anti fuzzy graphs products, which are adapted from fuzzy graphs products. In general, product of any two anti fuzzy graphs is an anti fuzzy graph. Product of any two strong anti fuzzy graphs is an anti fuzzy graph strong. Normal product of two anti fuzzy graph complete is a complete anti fuzzy graph. Other than that, different of anti fuzzy products are also discussed.

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18

Sufia Aziz. "Characteristic Graph vs Benzenoid Graph." Mathematical Journal of Interdisciplinary Sciences 7, no. 2 (2019): 135–47. http://dx.doi.org/10.15415/mjis.2019.72018.

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A characteristic graph is a tree representative of its corresponding benzenoid (cyclic) graph. It may contain necessary information of several properties of benzenoids. The PI-index of benzenoids and their characteristic graphs are compared by correlating it to a structural property (π-electron energy) of the benzenoids using MLR analysis. PI index being applicable to both trees and cyclic graphs, yielded required results for benzenoid and their characteristic graph.

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Et. al., PuruchothamaNayakiM. "Distance Based Topological Indices And Regular Graphs." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (2021): 5191–96. http://dx.doi.org/10.17762/turcomat.v12i3.2147.

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In this article, we are using the regular graph of even number of vertices and computing the distance balanced graphs. First we take a graph for satisfying regular definition and then we compute the Mostar index of that particular graph. If the Mostar index of that particular graph is zero, then the graph is said to be a distance balanced graph. So we discuss first distance balanced graph. Suppose if we delete one edge in that particular graph, that is non-regular graph, we can verify the balanced graph is whether distance balanced graph or not. We discuss and compute the Mostar index of certa

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20

Zeen El Deen, Mohamed R. "Enumeration of spanning trees in prisms of some graphs." Proyecciones (Antofagasta) 42, no. 2 (2023): 339–91. http://dx.doi.org/10.22199/issn.0717-6279-4664.

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In graph theory, a prism over a graph G is the cartesian product of the graph G with P₂. The purpose of this work is to investigate the complexity of the prisms of some path and cycle-related graphs. In particular, we obtain simpler and more explicit formulas for the complexity of a special class of prisms of path-related graphs: fan graph, ladder graph, the composition Pn[P₂] graph, and book graph. Moreover, we obtain straightforward formulas for the complexity of a special class of prisms of cycle-related graphs: wheel graph, gear graph, prism graph, n−crossed prism graph, mirror graph M(Cn)

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Fujita, Takaaki. "Claw-free Graph and AT-free Graph in Fuzzy, Neutrosophic, and Plithogenic Graphs." Information Sciences with Applications 5 (March 5, 2025): 40–55. https://doi.org/10.61356/j.iswa.2025.5502.

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Graph theory studies networks consisting of nodes (vertices) and their connections (edges), with various graph classes being extensively researched. This paper focuses on three specific graph classes: AT-Free Graphs, Claw-Free Graphs, and Triangle-Free Graphs. Additionally, it examines uncertain graph models, including Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Graphs, which are designed to address uncertainty in diverse applications. In this study, we introduce and analyze AT-Free Graphs, Claw-Free Graphs, and Triangle-Free Graphs within the framework of Fuzzy Graphs, investig

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Prabha, S. Celine, M. Palanivel, S. Amutha, et al. "Solutions of Detour Distance Graph Equations." Sensors 22, no. 21 (2022): 8440. http://dx.doi.org/10.3390/s22218440.

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Graph theory is a useful mathematical structure used to model pairwise relations between sensor nodes in wireless sensor networks. Graph equations are nothing but equations in which the unknown factors are graphs. Many problems and results in graph theory can be formulated in terms of graph equations. In this paper, we solved some graph equations of detour two-distance graphs, detour three-distance graphs, detour antipodal graphs involving with the line graphs.

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Ibarra, Sofía, and Luis Manuel Rivera. "The automorphism groups of some token graphs." Proyecciones (Antofagasta) 42, no. 6 (2023): 1627–51. http://dx.doi.org/10.22199/issn.0717-6279-5954.

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The token graphs of graphs have been studied at least from the 80’s with different names and by different authors. The Johnson graph J(n, k) is isomorphic to the k-token graph of the complete graph Kn. To our knowledge, the unique results about the automorphism groups of token graphs are for the case of the Johnson graphs. In this paper we begin the study of the automorphism groups of token graphs of another graphs. In particular we obtain the automorphism group of the k-token graph of the path graph Pn, for n 6≠ 2k. Also, we obtain the automorphism group of the 2-token graph of the following

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K.R., Sridhara, та Mallikarjun Basanna Kattimani. "The (𝑎,𝑏)− Status Indices of Central Graphs of Some Standard Graph". International Journal of Basic Sciences and Applied Computing 8, № 8 (2022): 12–17. http://dx.doi.org/10.35940/ijbsac.h0476.048822.

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The sum of shortest distance between a vertex 𝒖 from all other vertices of a graph 𝑮 is called the index of the vertex 𝒖 and is denoted by 𝝈(𝒖). In this article, we have obtained, the(𝒂,𝒃)− status index [3] of central graphs of some standard graphs namely star graph, complete graph, cycle graph, wheel graph and friendship graph. Using this new index, we have computed 9 standard status indices of all these central graphs of standard graphs.

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Shim, Sooyeon, Junghun Kim, Kahyun Park, and U. Kang. "Accurate graph classification via two-staged contrastive curriculum learning." PLOS ONE 19, no. 1 (2024): e0296171. http://dx.doi.org/10.1371/journal.pone.0296171.

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Given a graph dataset, how can we generate meaningful graph representations that maximize classification accuracy? Learning representative graph embeddings is important for solving various real-world graph-based tasks. Graph contrastive learning aims to learn representations of graphs by capturing the relationship between the original graph and the augmented graph. However, previous contrastive learning methods neither capture semantic information within graphs nor consider both nodes and graphs while learning graph embeddings. We propose TAG (Two-staged contrAstive curriculum learning for Gra

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Blinco, Andrew. "Theta graphs, graph decompositions and related graph labelling techniques." Bulletin of the Australian Mathematical Society 69, no. 1 (2004): 173–75. http://dx.doi.org/10.1017/s0004972700034377.

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Slilaty, Daniel. "Coloring permutation-gain graphs." Contributions to Discrete Mathematics 16, no. 1 (2021): 47–52. http://dx.doi.org/10.55016/ojs/cdm.v16i1.62717.

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Correspondence colorings of graphs were introduced in 2018 by Dvořák and Postle as a generalization of list colorings of graphs which generalizes ordinary graph coloring. Kim and Ozeki observed that correspondence colorings generalize various notions of signed-graph colorings which again generalizes ordinary graph colorings. In this note we state how correspondence colorings generalize Zaslavsky's notion of gain-graph colorings and then formulate a new coloring theory of permutation-gain graphs that sits between gain-graph coloring and correspondence colorings. Like Zaslavsky's gain-graph colo

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Zhang, Tong, Yun Wang, Zhen Cui, et al. "Deep Wasserstein Graph Discriminant Learning for Graph Classification." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 12 (2021): 10914–22. http://dx.doi.org/10.1609/aaai.v35i12.17303.

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Graph topological structures are crucial to distinguish different-class graphs. In this work, we propose a deep Wasserstein graph discriminant learning (WGDL) framework to learn discriminative embeddings of graphs in Wasserstein-metric (W-metric) matching space. In order to bypass the calculation of W-metric class centers in discriminant analysis, as well as better support batch process learning, we introduce a reference set of graphs (aka graph dictionary) to express those representative graph samples (aka dictionary keys). On the bridge of graph dictionary, every input graph can be projected

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Hanif, Muhammad Zeeshan, Naveed Yaqoob, Muhammad Riaz, and Muhammad Aslam. "Linear Diophantine fuzzy graphs with new decision-making approach." AIMS Mathematics 7, no. 8 (2022): 14532–56. http://dx.doi.org/10.3934/math.2022801.

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<abstract><p>The concept of linear Diophantine fuzzy set (LDFS) is a new mathematical tool for optimization, soft computing, and decision analysis. The aim of this article is to extend the notion of graph theory towards LDFSs. We initiate the idea of linear Diophantine fuzzy graph (LDF-graph) as a generalization of certain theoretical concepts including, q-rung orthopair fuzzy graph, Pythagorean fuzzy graph, and intuitionistic fuzzy graph. We extend certain properties of crisp graph theory towards LDF-graph including, composition, join, and union of LDF-graphs. We elucidate these o

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Sridhara, K.R., та Mallikarjun Basanna Kattimani Dr. "The (𝑎,𝑏)− Status Indices of Central Graphs of Some Standard Graph". International Journal of Basic Sciences and Applied Computing (IJBSAC) 8, № 8 (2022): 12–17. https://doi.org/10.35940/ijbsac.H0476.048822.

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<strong>Abstract:</strong> The sum of shortest distance between a vertex 𝒖 from all other vertices of a graph 𝑮 is called the index of the vertex 𝒖 and is denoted by 𝝈(𝒖). In this article, we have obtained, the(𝒂,𝒃)− status index [3] of central graphs of some standard graphs namely star graph, complete graph, cycle graph, wheel graph and friendship graph. Using this new index, we have computed 9 standard status indices of all these central graphs of standard graphs.

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31

Ismail, Sumarno, Isran K. Hasan, Tesya Sigar, and Salmun K. Nasib. "RAINBOW CONNECTION NUMBER AND TOTAL RAINBOW CONNECTION NUMBER OF AMALGAMATION RESULTS DIAMOND GRAPH(〖Br〗_4) AND FAN GRAPH(F_3)." BAREKENG: Jurnal Ilmu Matematika dan Terapan 16, no. 1 (2022): 023–30. http://dx.doi.org/10.30598/barekengvol16iss1pp023-030.

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If be a graph and edge coloring of G is a function , rainbow connection number is the minimum-k coloration of the rainbow on the edge of graph G and denoted by rc(G). Rainbow connection numbers can be applied to the result of operations on some special graphs, such as diamond graphs and fan graphs. Graph operation is a method used to obtain a new graph by combining two graphs. This study performed amalgamation operations to obtain rainbow connection numbers and rainbow-total-connection numbers in diamond graphs ( ) and fan graphs ( ) or . Based on the research, it is obtained that the rainbow-

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K, Radha, and Jasmine Kingsly A. "Cardinality and Isomorphic Properties of Hajós Graphs and Hajós Fuzzy Graphs." Indian Journal of Science and Technology 17, no. 37 (2024): 3871–80. https://doi.org/10.17485/IJST/v17i37.2492.

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Abstract <strong>Objectives:</strong> Fuzzy graphs allow uncertainty in the ideas characterizing vertices and edges to be included when modelling real-world scenarios into graph models. This study aims to introduce Hajós fuzzy graph, cardinality of Hajós graph and Hajós fuzzy graph and to explore many properties.<strong> Methods :</strong> Here, the Hajós construction is applied to two fuzzy graphs, and the Hajós fuzzy graph is defined by assigning membership values to all the edges and vertices of the newly formed fuzzy graph. Fuzzy graph cond

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Tamanna, Kumari, Kumar Kamal, and Agarwal Richa. "A STUDY OF STRUCTURE OF GRAPH INVARIANT WITH THEIR INDEPENDENCE NUMBERS AND CAYLEY GRAPHS." Soch – Mastnath Journal Of Science & Technology 17, no. 2 (2022): 1–8. https://doi.org/10.5281/zenodo.8009349.

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ABSTRACT In this paper the independence numbers and algebraic properties of graph invariant has been discussed and studied. The graph invariant is generalization of Petersen graphs whose independence numbers have been previously known. The authors studied the bounds for the independence number of different graph invariant and sub-classes of graph invariant, and exactly determine the independence number for other graph invariant and sub-classes of graph invariant. Authors also analysed the automorphism groups of the graph invariant.

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SINHA, DEEPA, and DEEPAKSHI SHARMA. "On Square and 2-path Signed Graph." Journal of Interconnection Networks 16, no. 01 (2016): 1550011. http://dx.doi.org/10.1142/s0219265915500115.

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A signed graph is an ordered pair [Formula: see text], where [Formula: see text] is a graph G = (V, E), called the underlying graph of S and [Formula: see text] is a function from the edge set E of Su into the set {+, -}, called the signature of S. In this paper, we characterize all those signed graphs whose 2-path signed graphs are isomorphic to their square signed graph along with algorithm to check the same. In other sections we find the characterization of signed graph S such that [Formula: see text] where D is a derived signed graph of the signed graph S such as: line signed graphs, total

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KAPOOR, SANJIV, and XIANG-YANG LI. "PROXIMITY STRUCTURES FOR GEOMETRIC GRAPHS." International Journal of Computational Geometry & Applications 20, no. 04 (2010): 415–29. http://dx.doi.org/10.1142/s0218195910003360.

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In this paper we study proximity graph structures like Delaunay triangulations based on geometric graphs, i.e. graphs which are subgraphs of the complete geometric graph. Given an arbitrary geometric graph G, we define Voronoi diagrams, Delaunay triangulations, relative neighborhood graphs, Gabriel graphs which are related to the graph structure and then study their complexities when G is a general geometric graph or G is some special graph derived from the application area of wireless networks. Besides being of fundamental interest these structures have applications in topology control for wi

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Manash Protim Borah. "Quasi- Laplacian energy of some novel classes of graphs." Communications on Applied Nonlinear Analysis 32, no. 7s (2025): 530–41. https://doi.org/10.52783/cana.v32.3462.

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We formulate the relationship of quasi-Laplacian energy of some novel classes of graphs with their corresponding original graphs. The novel graphs in our discussion are the -graph, -graph, -graph, total graph, and their join and corona operations graphs. The whole formulation is based on the relationship between quasi-Laplacian energy and the vertex degrees of the novel graph. It is also noted that quasi-Laplacian energy is closely related with the first Zagreb index, number of vertices and edges of the graph. The exact formulas of quasi-Laplacian energy of novel graphs are obtained in terms o

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Keerthi, G. Mirajkar* Bhagyashri R. Doddamani Priyanka Y. B. "THE REFORMULATED FIRST ZAGREB INDEX OF THE LINE GRAPHS OF THE SUBDIVISION GRAPH FOR CLASS OF GRAPHS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 5, no. 10 (2016): 144–49. https://doi.org/10.5281/zenodo.159334.

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The reformulated first Zagreb index is the edge version of first Zagreb index of chemical graph theory. The aim of this paper is to obtain an expression for the reformulated first Zagreb index of the some class of graphs such as Tadpole graph, Wheel graph, Ladder graph. Further we also obtain the reformulated first Zagreb index of the line graph, subdivision graph and line graph of subdivision graph for class of graphs.

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Li, Qiuping, Liangwen Tang, Qingyun Liu, and Mugang Lin. "A New Family of Multipartition Graph Operations and Its Applications in Constructing Several Special Graphs." Symmetry 17, no. 3 (2025): 467. https://doi.org/10.3390/sym17030467.

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A new family of graph operations based on multipartite graph with an arbitrary number of parts is defined and their applications are explored in this paper. The complete spectra of graphs derived from multipartite graphs are determined. Because the adjacency matrix of the multipartite graph is symmetric, we can use it to generate an unlimited number of special symmetric graphs. Methods for generating countless new families of integral graphs using these multipartite graph operations have been presented. By applying these multipartite graph operations, we can construct infinitely many orderener

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Ling, Yawen, Jianpeng Chen, Yazhou Ren, et al. "Dual Label-Guided Graph Refinement for Multi-View Graph Clustering." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 7 (2023): 8791–98. http://dx.doi.org/10.1609/aaai.v37i7.26057.

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With the increase of multi-view graph data, multi-view graph clustering (MVGC) that can discover the hidden clusters without label supervision has attracted growing attention from researchers. Existing MVGC methods are often sensitive to the given graphs, especially influenced by the low quality graphs, i.e., they tend to be limited by the homophily assumption. However, the widespread real-world data hardly satisfy the homophily assumption. This gap limits the performance of existing MVGC methods on low homophilous graphs. To mitigate this limitation, our motivation is to extract high-level vi

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Ali, Muhammad Asad, Muhammad Shoaib Sardar, Imran Siddique, and Dalal Alrowaili. "Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph." Journal of Chemistry 2021 (October 26, 2021): 1–12. http://dx.doi.org/10.1155/2021/7057412.

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A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double gra

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Kaladevi, V., R. Murugesan, and K. Pattabiraman. "First reformulated Zagreb indices of some classes of graphs." Carpathian Mathematical Publications 9, no. 2 (2018): 134–44. http://dx.doi.org/10.15330/cmp.9.2.134-144.

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A topological index of a graph is a parameter related to the graph; it does not depend on labeling or pictorial representation of the graph. Graph operations plays a vital role to analyze the structure and properties of a large graph which is derived from the smaller graphs. The Zagreb indices are the important topological indices found to have the applications in Quantitative Structure Property Relationship(QSPR) and Quantitative Structure Activity Relationship(QSAR) studies as well. There are various study of different versions of Zagreb indices. One of the most important Zagreb indices is t

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T. K., Jahfar, and Chithra A. V. "Energy and Randić energy of special graphs." Proyecciones (Antofagasta) 41, no. 4 (2022): 855–77. http://dx.doi.org/10.22199/issn.0717-6279-4616.

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In this paper, we determine the Randić energy of the m-splitting graph, the m-shadow graph and the m-duplicate graph of a given graph, m being an arbitrary integer. Our results allow the construction of an infinite sequence of graphs having the same Randić energy. Further, we determine some graph invariants like the degree Kirchhoff index, the Kemeny’s constant and the number of spanning trees of some special graphs. From our results, we indicate how to obtain infinitely many pairs of equienergetic graphs, Randić equienergetic graphs and also, infinite families of integral graphs.

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Firmansah, Fery, and Wed Giyarti. "Odd harmonious labeling on the amalgamation of the generalized double quadrilateral windmill graph." Desimal: Jurnal Matematika 4, no. 3 (2021): 373–78. http://dx.doi.org/10.24042/djm.v4i3.10823.

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Graph labeling is one of the topics of graph theory that is growing very rapidly both in terms of theory and application. A graph that satisfies the labeling property of odd harmonious is called an odd harmonious graph. The method used in this research is qualitative research by developing a theory and a new class of graphs from odd harmonious graphs. In this research, a new graph class construction will be given in the form of an amalgamation of the generalized double quadrilateral windmill graph. Furthermore, it will be proved that the amalgamation of the generalized double quadrilateral win

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Pattabiraman, K., and P. Kandan. "Weighted PI index of corona product of graphs." Discrete Mathematics, Algorithms and Applications 06, no. 04 (2014): 1450055. http://dx.doi.org/10.1142/s1793830914500554.

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In this paper, we present exact formula for the weighted PI index of corona product of two connected graphs in terms of other graph invariants including the PI index, first Zagreb index and second Zagreb index. Then, we apply our result to compute the weighted PI indices of t-fold bristled graph, bottleneck graph, sunlet graph, star graph, fan graph, wheel graph and some classes of bridge graphs.

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Singh, Priyanka, and Pratima Panigrahi. "On Self-Centeredness of Product of Graphs." International Journal of Combinatorics 2016 (August 7, 2016): 1–4. http://dx.doi.org/10.1155/2016/2508156.

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A graph G is said to be a self-centered graph if the eccentricity of every vertex of the graph is the same. In other words, a graph is a self-centered graph if radius and diameter of the graph are equal. In this paper, self-centeredness of strong product, co-normal product, and lexicographic product of graphs is studied in detail. The necessary and sufficient conditions for these products of graphs to be a self-centered graph are also discussed. The distance between any two vertices in the co-normal product of a finite number of graphs is also computed analytically.

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A. Antony mary, A., A. Amutha, and M. S. Franklin Thamil Selvi. "A Study on Slope Number of Certain Classes of Bipartite Graphs." International Journal of Engineering & Technology 7, no. 4.10 (2018): 440. http://dx.doi.org/10.14419/ijet.v7i4.10.21036.

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Graph drawing is the most important area of mathematics and computer science which combines methods from geometric graph theory and information visualization. Generally, graphs are represented to explore some intellectual ideas. Graph drawing is the familiar concept of graph theory. It has many quality measures and one among them is the slope number. Slope number problem is an optimization problem and is NP-hard to determine the slope number of any arbitrary graph. In the present paper, the investigation on slope number of bipartite graph is studied elaborately. Since the bipartite graphs crea

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Pramanik, L. K. "Centers in inserted graphs." Filomat 21, no. 2 (2007): 21–30. http://dx.doi.org/10.2298/fil0702021p.

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In this paper we study some concepts involving distance in inserted graphs with an emphasize on centers in inserted graphs. More precisely we prove that for every non-trivial connected graph H there exists a graph G such that H is the center of G and the inserted graph of H is the center of the inserted graph of G. Graphs which are the periphery of some inserted graph are characterized. .

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Coutino, Mario, Sundeep Prabhakar Chepuri, Takanori Maehara, and Geert Leus. "Fast Spectral Approximation of Structured Graphs with Applications to Graph Filtering." Algorithms 13, no. 9 (2020): 214. http://dx.doi.org/10.3390/a13090214.

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To analyze and synthesize signals on networks or graphs, Fourier theory has been extended to irregular domains, leading to a so-called graph Fourier transform. Unfortunately, different from the traditional Fourier transform, each graph exhibits a different graph Fourier transform. Therefore to analyze the graph-frequency domain properties of a graph signal, the graph Fourier modes and graph frequencies must be computed for the graph under study. Although to find these graph frequencies and modes, a computationally expensive, or even prohibitive, eigendecomposition of the graph is required, the

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Rice, Sean J., and Douglas J. Gillan. "Effects of Graphs on Text Comprehension." Proceedings of the Human Factors and Ergonomics Society Annual Meeting 44, no. 21 (2000): 3–443. http://dx.doi.org/10.1177/154193120004402117.

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Sources of information, from textbooks to multimedia encyclopedias combine text and graphics. This paper applies the construction-integration model of text comprehension to the processing of text and quantitative graphs. The model suggests that, when reading a graph that has information that is redundant with the text, a reader may directly connect the propositional information from the graph and the text due to overlap. When reading a graph that has information that elaborates on the text, a reader makes inferences to connect the propositional information from the graph and the text. Hypothes

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Prasetyo, Joko. "FAKTORISASI PADA GRAF REGULER." EDUPEDIA 4, no. 1 (2020): 75. http://dx.doi.org/10.24269/ed.v4i1.434.

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This research aims to: (1) know the criteria of a graph that has a -factor, (2) know the conditions of a regular graph that has a 1-factorization , (3) know the conditions of a regular graph that has a 2-factorization.This research is a qualitative descriptive study using the method of literature study or literature review where a study of books, scientific journals, and other literature languages is carried out relating to factorization on regular graphs. This research begins by discussing the definitions and examples of euler graphs and regular bipartite multigraphs. Next in reviewing the te

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