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Journal articles on the topic 'Simple graph'

Author: Grafiati

Published: 18 May 2024

Last updated: 25 July 2025

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1

Voorhees, Burton, and Alex Murray. "Fixation probabilities for simple digraphs." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2154 (2013): 20120676. http://dx.doi.org/10.1098/rspa.2012.0676.

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The problem of finding birth–death fixation probabilities for configurations of normal and mutants on an N -vertex graph is formulated in terms of a Markov process on the 2 N -dimensional state space of possible configurations. Upper and lower bounds on the fixation probability after any given number of iterations of the birth–death process are derived in terms of the transition matrix of this process. Consideration is then specialized to a family of graphs called circular flows, and we present a summation formula for the complete bipartite graph, giving the fixation probability for an arbitra

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2

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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TROTTA, BELINDA. "RESIDUAL PROPERTIES OF SIMPLE GRAPHS." Bulletin of the Australian Mathematical Society 82, no. 3 (2010): 488–504. http://dx.doi.org/10.1017/s0004972710000420.

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AbstractClark et al. [‘The axiomatizability of topological prevarieties’, Adv. Math.218 (2008), 1604–1653] have shown that, for k≥2, there exists a Boolean topological graph that is k-colourable but not topologically k-colourable; that is, for every ϵ>0, it cannot be coloured by a paintbrush of width ϵ. We generalize this result to show that, for k≥2, there is a Boolean topological graph that is 2-colourable but not topologically k-colourable. This graph is an inverse limit of finite graphs which are shown to exist by an Erdős-style probabilistic argument of Hell and Nešetřil [‘The core of

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Abughazalah, Nabilah, Naveed Yaqoob, and Asif Bashir. "Cayley Graphs over LA-Groups and LA-Polygroups." Mathematical Problems in Engineering 2021 (May 10, 2021): 1–9. http://dx.doi.org/10.1155/2021/4226232.

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The purpose of this paper is the study of simple graphs that are generalized Cayley graphs over LA-polygroups GCLAP − graphs . In this regard, we construct two new extensions for building LA-polygroups. Then, we define Cayley graph over LA-group and GCLAP-graph. Further, we investigate a few properties of them to show that each simple graph of order three, four, and five (except cycle graph of order five which may or may not be a GCLAP-graph) is a GCLAP-graph and then we prove this result.

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Amanto, Amanto, Notiragayu Notiragayu, La Zakaria, and Wamiliana Wamiliana. "The relationship of the formulas for the number of connected vertices labeled graphs with order five and order six without loops." Desimal: Jurnal Matematika 4, no. 3 (2021): 357–64. http://dx.doi.org/10.24042/djm.v4i3.10006.

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Given a graph with n points and m lines. If each vertex is labeled, then it can be constructed many graphs, connected, or disconnected graphs. A graph G is called a connected graph if there is at least one path that connects a pair of vertices in G. In addition, the graph formed may be simple or not simple. A simple graph is a graph that does not contain loops or parallel lines. A loop is a line that connects a point to itself, and a parallel line is two or more lines that connect the same pair of points. This paper will discuss the relationship between the formula patterns for calculating the

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Alzubaidi, Husniyah, Ljubiša D. R. Kočinac, and Hakeem A. Othman. "On Topologies on Simple Graphs and Their Applications in Radar Chart Methods." Axioms 14, no. 3 (2025): 178. https://doi.org/10.3390/axioms14030178.

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This paper introduces a novel topology (upper approximated G-topology) on vertex sets of graphs using rough upper approximation neighborhoods, extending prior work on graph-induced topologies. Key results include characterizing discrete/indiscrete topologies for complete graphs, cycle graphs, and bipartite graphs (Theorems 1–3). The discrete topology for cycle graphs Cn, n>5, is particularly insightful. Exploring further, we delve into the continuity and isomorphism of graph mappings. Subsequently, we apply these findings to enhance radar chart graphical methods through the analysis of corr

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Ali, Akbar. "Tetracyclic graphs with maximum second Zagreb index: A simple approach." Asian-European Journal of Mathematics 11, no. 05 (2018): 1850064. http://dx.doi.org/10.1142/s179355711850064x.

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In the chemical graph theory, graph invariants are usually referred to as topological indices. The second Zagreb index (denoted by [Formula: see text]) is one of the most studied topological indices. For [Formula: see text], let [Formula: see text] be the collection of all non-isomorphic connected graphs with [Formula: see text] vertices and [Formula: see text] edges (such graphs are known as tetracyclic graphs). Recently, Habibi et al. [Extremal tetracyclic graphs with respect to the first and second Zagreb indices, Trans. on Combin. 5(4) (2016) 35–55.] characterized the graph having maximum

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BAHR, PATRICK. "Convergence in infinitary term graph rewriting systems is simple." Mathematical Structures in Computer Science 28, no. 8 (2018): 1363–414. http://dx.doi.org/10.1017/s0960129518000166.

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Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by emulating duplication via sharing. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can be used to model non-strict evaluation. In this paper, we unify term graph rewriting and infinitary term rewriting thereby addressing both components of lazy evaluation: non-strictness and sharing. In contrast to previous attempts to formalise infinitary term graph rewriting, our approach is based on a simple and natural generalisation of the m

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9

KHEIRABADI, M., and A. R. MOGHADDAMFAR. "RECOGNIZING SOME FINITE SIMPLE GROUPS BY NONCOMMUTING GRAPH." Journal of Algebra and Its Applications 11, no. 04 (2012): 1250077. http://dx.doi.org/10.1142/s0219498812500776.

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Let G be a nonabelian group. We define the noncommuting graph ∇(G) of G as follows: its vertex set is G\Z(G), the noncentral elements of G, and two distinct vertices x and y of ∇(G) are joined by an edge if and only if x and y do not commute as elements of G, i.e. [x, y] ≠ 1. The finite group L is said to be recognizable by noncommuting graph if, for every finite group G, ∇(G) ≅ ∇ (L) implies G ≅ L. In the present article, it is shown that the noncommuting graph of a group with trivial center can determine its prime graph. From this, the following theorem is derived. If two finite groups with

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Malik, M. Aslam, and M. Khalid Mahmood. "On Simple Graphs Arising from Exponential Congruences." Journal of Applied Mathematics 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/292895.

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We introduce and investigate a new class of graphs arrived from exponential congruences. For each pair of positive integersaandb, letG(n)denote the graph for whichV={0,1,…,n−1}is the set of vertices and there is an edge betweenaandbif the congruenceax≡b (mod n)is solvable. Letn=p1k1p2k2⋯prkrbe the prime power factorization of an integern, wherep1<p2<⋯<prare distinct primes. The number of nontrivial self-loops of the graphG(n)has been determined and shown to be equal to∏i=1r(ϕ(piki)+1). It is shown that the graphG(n)has2rcomponents. Further, it is proved that the componentΓpof the simp

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Yang, Xiaocheng, Mingyu Yan, Shirui Pan, Xiaochun Ye, and Dongrui Fan. "Simple and Efficient Heterogeneous Graph Neural Network." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 9 (2023): 10816–24. http://dx.doi.org/10.1609/aaai.v37i9.26283.

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Heterogeneous graph neural networks (HGNNs) have the powerful capability to embed rich structural and semantic information of a heterogeneous graph into node representations. Existing HGNNs inherit many mechanisms from graph neural networks (GNNs) designed for homogeneous graphs, especially the attention mechanism and the multi-layer structure. These mechanisms bring excessive complexity, but seldom work studies whether they are really effective on heterogeneous graphs. In this paper, we conduct an in-depth and detailed study of these mechanisms and propose the Simple and Efficient Heterogeneo

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Cui, Yan, and Chao Dong Cui. "Study on Necessary and Sufficient Conditions for Euler Graph and Hamilton Graph." Advanced Materials Research 1044-1045 (October 2014): 1357–61. http://dx.doi.org/10.4028/www.scientific.net/amr.1044-1045.1357.

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Three theorems are proposed in this paper. The first theorem is that a connected undirected graph G is an Euler graph if and only if G can be expressed as the union of two circles without overlapped sides. Namely, equation satisfies. The second theorem is that a connected simple undirected graph is a Hamilton graph if and only if G contains a sub-graph generated by union of circles of sub-graphs derived from two endpoints of common side. Namely, the equation satisfies (meaning of symbols in the equations see main body of this paper). The third theorem is that a connected simple undirected grap

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Dutta, Supriyo, Bibhas Adhikari, and Subhashish Banerjee. "Condition for zero and nonzero discord in graph Laplacian quantum states." International Journal of Quantum Information 17, no. 02 (2019): 1950018. http://dx.doi.org/10.1142/s0219749919500187.

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This work is at the interface of graph theory and quantum mechanics. Quantum correlations epitomize the usefulness of quantum mechanics. Quantum discord is an interesting facet of bipartite quantum correlations. Earlier, it was shown that every combinatorial graph corresponds to quantum states whose characteristics are reflected in the structure of the underlined graph. A number of combinatorial relations between quantum discord and simple graphs were studied. To extend the scope of these studies, we need to generalize the earlier concepts applicable to simple graphs to weighted graphs, corres

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Azari, M., and A. Iranmanesh. "On the edge-Wiener index of the disjunctive product of simple graphs." Algebra and Discrete Mathematics 30, no. 1 (2020): 1–14. http://dx.doi.org/10.12958/adm242.

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The edge-Wiener index of a simple connected graph G is defined as the sum of distances between all pairs of edges of G where the distance between two edges in G is the distance between the corresponding vertices in the line graph of G. In this paper, we study the edge-Wiener index under the disjunctive product of graphs and apply our results to compute the edge-Wiener index for the disjunctive product of paths and cycles.

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BURNESS, TIMOTHY C., and ELISA COVATO. "ON THE PRIME GRAPH OF SIMPLE GROUPS." Bulletin of the Australian Mathematical Society 91, no. 2 (2014): 227–40. http://dx.doi.org/10.1017/s0004972714000707.

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AbstractLet $G$ be a finite group, let ${\it\pi}(G)$ be the set of prime divisors of $|G|$ and let ${\rm\Gamma}(G)$ be the prime graph of $G$. This graph has vertex set ${\it\pi}(G)$, and two vertices $r$ and $s$ are adjacent if and only if $G$ contains an element of order $rs$. Many properties of these graphs have been studied in recent years, with a particular focus on the prime graphs of finite simple groups. In this note, we determine the pairs $(G,H)$, where $G$ is simple and $H$ is a proper subgroup of $G$ such that ${\rm\Gamma}(G)={\rm\Gamma}(H)$.

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Türkmen, Burcu Nişancı, and Gülçin Karaca. "Finitely Generated Simple Graphs." International Journal of Applied Sciences and Smart Technologies 5, no. 2 (2023): 191–200. http://dx.doi.org/10.24071/ijasst.v5i2.6739.

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In this paper, Kirchhoff, Hyper-Wiener, Randic, Szeged, Pi index calculations of finitely generated (cyclic) simple graphs on the samples were made and classification of some finitely generated (cyclic) groups was achieved with the help of graph theory.

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Asif, Sufyan, Muhammad Khalid Mahmood, Amal S. Alali, and Abdullah A. Zaagan. "Structures and applications of graphs arising from congruences over moduli." AIMS Mathematics 9, no. 8 (2024): 21786–98. http://dx.doi.org/10.3934/math.20241059.

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<p>For any positive integer $ \mathrm{n} $, let $ \mathrm{M_{p}} $ contain the prime numbers less than $ \mathrm{n} $. Assuming $ \mathrm{M_{p}} $ as the set of moduli, we draw a graph with the vertex set $ \{1, 2, 3, \cdots, \mathrm{n}\} $, and an edge will be built between the vertices $ \mathrm{p} $ and $ \mathrm{q} $ if and only if $ \mathrm{p}\equiv (\mathrm{q}\; mod\; \mathrm{m}) $ for some $ \mathrm{m}\in $ $ \mathrm{M_{p}}. $ We call this graph a prime congruence simple graph and label this graph as $ \mathrm{G}(\mathrm{n}, \mathrm{M}_{p}) $. The objective of this work is to char

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18

Nada A Laabi. "Subring in Graph Theory." Advances in Nonlinear Variational Inequalities 27, no. 4 (2024): 284–87. http://dx.doi.org/10.52783/anvi.v27.1526.

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In our study, we delved into the intricacies of graph theory by exploring the properties of subrings within various types of graphs. By focusing on prime graphs and simple graphs, we unraveled the complex relationship between subring-prime graphs. Additionally, we delved into the concept of homomorphism within both simple subring graphs and prime subring graphs, adding depth to our analysis.

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Imran, Muhammad, Murat Cancan, Muhammad Faisal Nadeem, and Yasir Ali. "Further results on edge irregularity strength of some graphs." Proyecciones (Antofagasta) 43, no. 1 (2024): 133–51. http://dx.doi.org/10.22199/issn.0717-6279-6175.

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The focal point of this paper is to precisely ascertain the edge irregularity strength of various finite, simple, and undirected captivating graphs, including splitting graph, shadow graph, jewel graph, jellyfish graph, and $m$ copies of 4-pan graph.

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Hart, James, and Brian Frazier. "Finite Simple Graphs and Their Associated Graph Lattices." Theory and Applications of Graphs 5, no. 2 (2018): 1–20. http://dx.doi.org/10.20429/tag.2018.050206.

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T. Lavanya. "Extended Reverse R Degrees of Vertices and Extended Reverse R indices of Graphs." Communications on Applied Nonlinear Analysis 31, no. 5s (2024): 110–17. http://dx.doi.org/10.52783/cana.v31.1005.

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A topological representation of a molecule is called molecular graph. A molecular graph is a collection of points representing the atoms in the molecule and set of lines represent the covalent bonds. Topological indices gather data from the graph of molecule and help to foresee properties of the concealing molecule. All the degree based topological indices have been defined through classical degree concept. In this paper, we define a novel degree concept for a vertex of a simple connected graph: Extended Reverse R degree and also, we define Extended Reverse R indices of a simple connected grap

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Zheng, Haoran, Jieming Shi, and Renchi Yang. "GraSP: Simple Yet Effective Graph Similarity Predictions." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 21 (2025): 22884–92. https://doi.org/10.1609/aaai.v39i21.34450.

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Graph similarity computation (GSC) is to calculate the similarity between one pair of graphs, which is a fundamental problem with fruitful applications in the graph community. In GSC, graph edit distance (GED) and maximum common subgraph (MCS) are the two most adopted similarity metrics, both of which are NP-hard to compute. Instead of calculating the exact values, state-of-the-art solutions resort to leveraging graph neural networks (GNNs) to learn data-driven models for the estimation of GED and MCS. Most of them are built on components involving node-level interactions crossing graphs, whic

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Voorhees, Burton, and Bergerud Ryder. "Simple graph models of information spread in finite populations." Royal Society Open Science 2, no. 5 (2015): 150028. http://dx.doi.org/10.1098/rsos.150028.

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We consider several classes of simple graphs as potential models for information diffusion in a structured population. These include biases cycles, dual circular flows, partial bipartite graphs and what we call ‘single-link’ graphs. In addition to fixation probabilities, we study structure parameters for these graphs, including eigenvalues of the Laplacian, conductances, communicability and expected hitting times. In several cases, values of these parameters are related, most strongly so for partial bipartite graphs. A measure of directional bias in cycles and circular flows arises from the no

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Yurttas Gunes, Aysun, Hacer Ozden Ayna, and Ismail Naci Cangul. "The Effect of Vertex and Edge Removal on Sombor Index." Symmetry 16, no. 2 (2024): 170. http://dx.doi.org/10.3390/sym16020170.

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A vertex degree based topological index called the Sombor index was recently defined in 2021 by Gutman and has been very popular amongst chemists and mathematicians. We determine the amount of change of the Sombor index when some elements are removed from a graph. This is done for several graph elements, including a vertex, an edge, a cut vertex, a pendant edge, a pendant path, and a bridge in a simple graph. Also, pendant and non-pendant cases are studied. Using the obtained formulae successively, one can find the Sombor index of a large graph by means of the Sombor indices of smaller graphs

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Petrenjuk, Volodymyr, and Dmytro Petreniuk. "On the Synthesis of Planar Graphs with Given Properties." Cybernetics and Computer Technologies, no. 2 (June 6, 2025): 17–36. https://doi.org/10.34229/2707-451x.25.2.2.

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The problem of studying the structural properties of planar subgraphs G\v, where v is an arbitrary vertex of a graph G of undirected genus, is considered, using cell chains that connect limit cycles with points of a given set M of the graph G\v. Through the sum of the minimum in length and a number of cell chains covering M, we determine the cell distance of a given subset of the set of points of graph G. The goal is to synthesize planar graphs of a certain subset of points with a fixed length of the cell distance from at least two graphs with subsets of points of a smaller cell distance by id

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Munira W. Mahan. "Harmonic and Zagreb Polynomials and Their Applications on Chemical Nano-Structures." Advances in Nonlinear Variational Inequalities 28, no. 7s (2025): 250–56. https://doi.org/10.52783/anvi.v28.4501.

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The graph ???? consists of an ordered pair (????, ????), where ???? represents a nonempty set of elements called vertices for graph ????, and ???? is a family of unordered pairs that may be free of vertices in graph ???? and is called edges for graph ????. G called a simple graph if has not loops and without parallel edges, all graphs that used in this paper are simple graph. The degree of a vertex is number of edges E(G) at that vertex V(G) or V(u) where and are denoted for degree of vertex [1] [2].

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Guo, Hongyu, and Yongyi Mao. "Interpolating Graph Pair to Regularize Graph Classification." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (2023): 7766–74. http://dx.doi.org/10.1609/aaai.v37i6.25941.

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We present a simple and yet effective interpolation-based regularization technique, aiming to improve the generalization of Graph Neural Networks (GNNs) on supervised graph classification. We leverage Mixup, an effective regularizer for vision, where random sample pairs and their labels are interpolated to create synthetic images for training. Unlike images with grid-like coordinates, graphs have arbitrary structure and topology, which can be very sensitive to any modification that alters the graph's semantic meanings. This posts two unanswered questions for Mixup-like regularization schemes:

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Deb, Swakshar, Sejuti Rahman, and Shafin Rahman. "SEA-GWNN: Simple and Effective Adaptive Graph Wavelet Neural Network." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 10 (2024): 11740–48. http://dx.doi.org/10.1609/aaai.v38i10.29058.

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The utilization of wavelet-based techniques in graph neural networks (GNNs) has gained considerable attention, particularly in the context of node classification. Although existing wavelet-based approaches have shown promise, they are constrained by their reliance on pre-defined wavelet filters, rendering them incapable of effectively adapting to signals that reside on graphs based on tasks at hand. Recent research endeavors address this issue through the introduction of a wavelet lifting transform. However, this technique necessitates the use of bipartite graphs, causing a transformation of t

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Koch, Sebastian. "Underlying Simple Graphs." Formalized Mathematics 27, no. 3 (2019): 237–59. http://dx.doi.org/10.2478/forma-2019-0023.

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Summary In this article the notion of the underlying simple graph of a graph (as defined in [8]) is formalized in the Mizar system [5], along with some convenient variants. The property of a graph to be without decorators (as introduced in [7]) is formalized as well to serve as the base of graph enumerations in the future.

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Van Mieghem, Piet. "PATHS IN THE SIMPLE RANDOM GRAPH AND THE WAXMAN GRAPH." Probability in the Engineering and Informational Sciences 15, no. 4 (2001): 535–55. http://dx.doi.org/10.1017/s0269964801154070.

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The Waxman graphs are frequently chosen in simulations as topologies resembling communications networks. For the Waxman graphs, we present analytic, exact expressions for the link density (average number of links) and the average number of paths between two nodes. These results show the similarity of Waxman graphs to the simpler class G>p(N). The first result enables one to compare simulations performed on the Waxman graph with those on other graphs with same link density. The average number of paths in Waxman graphs can be useful to dimension (or estimate) routing paths in networks. Althou

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Wu, Tongsuo, and Li Chen. "Simple Graphs and Zero-divisor Semigroups." Algebra Colloquium 16, no. 02 (2009): 211–18. http://dx.doi.org/10.1142/s1005386709000212.

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In this paper, we provide examples of graphs which uniquely determine a zero-divisor semigroup. We show two classes of graphs that have no corresponding semigroups. Especially, we prove that no complete r-partite graph together with two or more end vertices (each linked to distinct vertices) has corresponding semigroups.

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Nieva, Alex Ralph, and Karen P. Nocum. "On Some Properties of Non-traceable Cubic Bridge Graph." European Journal of Pure and Applied Mathematics 15, no. 4 (2022): 1536–48. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4453.

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Graphs considered in this paper are simple finite undirected graphs without loops or multiple edges. A simple graphs where each vertex has degree 3 is called cubic graphs. A cubic graphs, that is, 1-connected or cubic bridge graph is traceable if its contains Hamiltonian path otherwise, non-traceable. In this paper, we introduce a new family of cubic graphs called Non-Traceable Cubic Bridge Graph (NTCBG) that satisfy the conjecture of Zoeram and Yaqubi (2017). In addition, we defined two important connected component of NTCBG that is, central fragment that give assurance for a graph to be non-

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Journal, Baghdad Science. "Tadpole Domination in Graphs." Baghdad Science Journal 15, no. 4 (2018): 466–71. http://dx.doi.org/10.21123/bsj.15.4.466-471.

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A new type of the connected domination parameters called tadpole domination number of a graph is introduced. Tadpole domination number for some standard graphs is determined, and some bounds for this number are obtained. Additionally, a new graph, finite, simple, undirected and connected, is introduced named weaver graph. Tadpole domination is calculated for this graph with other families of graphs.

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Alrowaili, Dalal Awadh, Uzma Ahmad, Saira Hameeed, and Muhammad Javaid. "Graphs with mixed metric dimension three and related algorithms." AIMS Mathematics 8, no. 7 (2023): 16708–23. http://dx.doi.org/10.3934/math.2023854.

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<abstract><p>Let $ G = (V, E) $ be a simple connected graph. A vertex $ x\in V(G) $ resolves the elements $ u, v\in E(G)\cup V(G) $ if $ d_G(x, u)\neq d_G(x, v) $. A subset $ S\subseteq V(G) $ is a mixed metric resolving set for $ G $ if every two elements of $ G $ are resolved by some vertex of $ S $. A set of smallest cardinality of mixed metric generator for $ G $ is called the mixed metric dimension. In this paper trees and unicyclic graphs having mixed dimension three are classified. The main aim is to investigate the structure of a simple connected graph having mixed dimensio

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Aneela, M. Khalid Mahmood, and Daud Ahmad. "A SPECIAL CLASS OF GRAPHS EMERGING FROM QUATERNION GROUPS." JP Journal of Algebra, Number Theory and Applications 64, no. 4 (2025): 379–94. https://doi.org/10.17654/0972555525020.

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This work explores new graphs constructed on generalized Quaternion groups . The vertices are the conjugacy classes of and there will be an edge between the two conjugacy classes if their orders are distinct. We define this simple graph as order structured conjugacy class simple graph (OSCSG), labelled by . In this research, we characterize the proposed graph and prove that for , the closure of can never be a complete graph. Its complement, always contains a maximum complete subgraph for . Moreover, for , the upper bound of average distance is determined. Finally, the bipartite and tri-partite

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Thalavayalil, Timmy Tomy, and Sudev Naduvath. "A study on coarse deg-centric graphs." Gulf Journal of Mathematics 16, no. 2 (2024): 171–82. http://dx.doi.org/10.56947/gjom.v16i2.1877.

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The coarse deg-centric graph of a simple, connected graph G, denoted by Gcd, is a graph constructed from G such that V(Gcd) = V(G) and E(Gcd) = {vi vj : dG( vi, vj) > degG(vi)}. This paper introduces and discusses the concepts of coarse deg-centric graphs and iterated coarse deg-centrication of a graph. It also presents the properties and structural characteristics of coarse deg-centric graphs of some graph families.

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WAN, PENG-JUN, KHALED M. ALZOUBI, and OPHIR FRIEDER. "A SIMPLE HEURISTIC FOR MINIMUM CONNECTED DOMINATING SET IN GRAPHS." International Journal of Foundations of Computer Science 14, no. 02 (2003): 323–33. http://dx.doi.org/10.1142/s0129054103001753.

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Let α2(G), γ(G) and γc(G) be the 2-independence number, the domination number, and the connected domination number of a graph G respectively. Then α2(G) ≤ γ (G) ≤ γc(G). In this paper , we present a simple heuristic for Minimum Connected Dominating Set in graphs. When running on a graph G excluding Km (the complete graph of order m) as a minor, the heuristic produces a connected dominating set of cardinality at most 7α2(G) - 4 if m = 3, or at most [Formula: see text] if m ≥ 4. In particular, if running on a planar graph G, the heuristic outputs a connected dominating set of cardinality at most

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Su, Huadong, and Yangjiang Wei. "Semipotent Rings Whose Unit Graphs Are Planar." Algebra Colloquium 27, no. 02 (2020): 311–18. http://dx.doi.org/10.1142/s1005386720000255.

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The unit graph of a ring is the simple graph whose vertices are the elements of the ring and where two distinct vertices are adjacent if and only if their sum is a unit of the ring. A simple graph is said to be planar if it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In this note, we completely characterize the semipotent rings whose unit graphs are planar. As a consequence, we list all semilocal rings with planar unit graphs.

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Ouadid, Y., B. Elbalaoui, M. Boutaounte, M. Fakir, and B. Minaoui. "Handwritten tifinagh character recognition using simple geometric shapes and graphs." Indonesian Journal of Electrical Engineering and Computer Science 13, no. 2 (2019): 598–605. https://doi.org/10.11591/ijeecs.v13.i2.pp598-605.

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In this paper, a graph based handwritten Tifinagh character recognition system is presented. In preprocessing Zhang Suen algorithm is enhanced. In features extraction, a novel key point extraction algorithm is presented. Images are then represented by adjacency matrices defining graphs where nodes represent feature points extracted by a novel algorithm. These graphs are classified using a graph matching method. Experimental results are obtained using two databases to test the effectiveness. The system shows good results in terms of recognition rate.

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40

Galán, Severino F. "Simple decentralized graph coloring." Computational Optimization and Applications 66, no. 1 (2016): 163–85. http://dx.doi.org/10.1007/s10589-016-9862-9.

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Ouadid, Youssef, Abderrahmane Elbalaoui, Mehdi Boutaounte, Mohamed Fakir, and Brahim Minaoui. "Handwritten tifinagh character recognition using simple geometric shapes and graphs." Indonesian Journal of Electrical Engineering and Computer Science 13, no. 2 (2019): 598. http://dx.doi.org/10.11591/ijeecs.v13.i2.pp598-605.

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<p>In this paper, a graph based handwritten Tifinagh character recognition system is presented. In preprocessing Zhang Suen algorithm is enhanced. In features extraction, a novel key point extraction algorithm is presented. Images are then represented by adjacency matrices defining graphs where nodes represent feature points extracted by a novel algorithm. These graphs are classified using a graph matching method. Experimental results are obtained using two databases to test the effectiveness. The system shows good results in terms of recognition rate.</p>

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42

Beaufays, Françoise, and Eric A. Wan. "Relating Real-Time Backpropagation and Backpropagation-Through-Time: An Application of Flow Graph Interreciprocity." Neural Computation 6, no. 2 (1994): 296–306. http://dx.doi.org/10.1162/neco.1994.6.2.296.

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We show that signal flow graph theory provides a simple way to relate two popular algorithms used for adapting dynamic neural networks, real-time backpropagation and backpropagation-through-time. Starting with the flow graph for real-time backpropagation, we use a simple transposition to produce a second graph. The new graph is shown to be interreciprocal with the original and to correspond to the backpropagation-through-time algorithm. Interreciprocity provides a theoretical argument to verify that both flow graphs implement the same overall weight update.

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Wang, Weizhong, and Dong Yang. "Bounds for Incidence Energy of Some Graphs." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/757542.

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LetGbe a simple graph. The incidence energy (IEfor short) ofGis defined as the sum of the singular values of the incidence matrix. In this paper, a new upper bound forIEof graphs in terms of the maximum degree is given. Meanwhile, bounds forIEof the line graph of a semiregular graph and the paraline graph of a regular graph are obtained.

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Ghorbani, Modjtaba, Matthias Dehmer, Shaghayegh Rahmani, and Mina Rajabi-Parsa. "A Survey on Symmetry Group of Polyhedral Graphs." Symmetry 12, no. 3 (2020): 370. http://dx.doi.org/10.3390/sym12030370.

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Every three-connected simple planar graph is a polyhedral graph and a cubic polyhedral graph with pentagonal and hexagonal faces is called as a classical fullerene. The aim of this paper is to survey some results about the symmetry group of cubic polyhedral graphs. We show that the order of symmetry group of such graphs divides 240.

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Solomko, Viktoriia, and Vladyslav Sobolev. "Constructing the Mate of Cospectral 5-regular Graphs with and without a Perfect Matching." Mohyla Mathematical Journal 4 (May 19, 2022): 24–27. http://dx.doi.org/10.18523/2617-70804202124-27.

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The problem of finding a perfect matching in an arbitrary simple graph is well known and popular in graph theory. It is used in various fields, such as chemistry, combinatorics, game theory etc. The matching of M in a simple graph G is a set of pairwise nonadjacent edges, ie, those that do not have common vertices. Matching is called perfect if it covers all vertices of the graph, ie each of the vertices of the graph is incidental to exactly one of the edges. By Koenig's theorem, regular bipartite graphs of positive degree always have perfect matching. However, graphs that are not bipartite ne

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Montenegro, Eduardo, Eduardo Cabrera, José González Campos, and Ronald Manríquez Peñafiel. "Linear representation of a graph." Boletim da Sociedade Paranaense de Matemática 37, no. 4 (2018): 97–102. http://dx.doi.org/10.5269/bspm.v37i4.32949.

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In this paper the linear representation of a graph is defined. A linear representation of a graph is a subgroup of $GL(p,\mathbb{R})$, the group of invertible matrices of order $ p $ and real coefficients. It will be demonstrated that every graph admits a linear representation. In this paper, simple and finite graphs will be used, framed in the graphs theory's area

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Holme, Petter, and Mikael Huss. "Substance graphs are optimal simple-graph representations of metabolism." Chinese Science Bulletin 55, no. 27-28 (2010): 3161–68. http://dx.doi.org/10.1007/s11434-010-4086-3.

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V.R.Kulli. "General Fifth M-Zagreb Indices and Fifth M-Zagreb Polynomials of PAMAM Dendrimers." International Journal of Fuzzy Mathematical Archive 13, no. 01 (2017): 99–103. http://dx.doi.org/10.22457/ijfma.v13n1a10.

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A molecular graph or a chemical graph is a simple graph related to the structure of a chemical compound. In this paper, we introduce the general fifth M-Zagreb indices and fifth M3-Zagreb index and their polynomials of a molecular graph. Also we compute the general fifth M-Zagreb indices and fifth M3-Zagreb index of PAMAM dendrimer graphs. Finally, we compute the fifth M3-Zagreb polynomial of PAMAM dendrimer graphs.

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Muhammad, Ibrahim, та Abubakar Umar. "Permutation graphs with co-inversion on Γ<sub>1</sub> - non-deranged permutations". Caliphate Journal of Science and Technology 5, № 2 (2023): 127–31. http://dx.doi.org/10.4314/cajost.v5i2.6.

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In this paper, we define permutation graphs on Γ1 -non-deranged permutations using the set of co-inversion as edge set, and the values of permutation as the set of vertices. From the graphs, we observed that diameter and radius of the graph of any ω1 is one, the graph of any ωp-1 ∈ GΓ1p simple, the graph of ω1 is completed and other properties of the graphs were also observed.

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Ediz, Süleyman. "On R degrees of vertices and R indices of graphs." International Journal of Advanced Chemistry 5, no. 2 (2017): 70. http://dx.doi.org/10.14419/ijac.v5i2.7973.

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Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: R degree. And also we define R indices of a simple connected graph by using the R degree concept. We compute the R indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.

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