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Journal articles on the topic 'Associated graph'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 July 2025

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1

Chen, X. Y., A. R. Moghaddamfar, and M. Zohourattar. "Some properties of various graphs associated with finite groups." Algebra and Discrete Mathematics 31, no. 2 (2021): 195–211. http://dx.doi.org/10.12958/adm1197.

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In this paper we investigate some properties of the power graph and commuting graph associated with a finite group, using their tree-numbers. Among other things, it is shown that the simple group L2(7) can be characterized through the tree-number of its power graph. Moreover, the classification of groups with power-free decomposition is presented. Finally, we obtain an explicit formula concerning the tree-number of commuting graphs associated with the Suzuki simple groups.

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Najmuddin, Nabilah, Nor Haniza Sarmin, and Ahmad Erfanian. "General Form of Domination Polynomial for Two Types of Graphs Associated to Dihedral Groups." MATEMATIKA 35, no. 2 (2019): 149–55. http://dx.doi.org/10.11113/matematika.v35.n2.1106.

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A domination polynomial is a type of graph polynomial in which its coefficients represent the number of dominating sets in the graph. There are many researches being done on the domination polynomial of some common types of graphs but not yet for graphs associated to finite groups. Two types of graphs associated to finite groups are the conjugate graph and the conjugacy class graph. A graph of a group G is called a conjugate graph if the vertices are non-central elements of G and two distinct vertices are adjacent if they are conjugate to each other. Meanwhile, a conjugacy class graph of a gro

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3

Ansari, Moin, Azeem Haidar, and Ali Koam. "On a Graph Associated to UP-Algebras." Mathematical and Computational Applications 23, no. 4 (2018): 61. http://dx.doi.org/10.3390/mca23040061.

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In this article, we introduce the concept of graphs associated with commutative UP-algebra, which we say is a UP-graph whose vertices are the elements of commutative UP-algebra and whose edges are the association of two vertices, that is two elements from commutative UP-algebra. We also define a graph of equivalence classes of a commutative UP-algebra and prove some related results based on the algebraic properties of the graph. We show that two graphs are the same and complete bipartite if they are formed by equivalence classes of UP-algebra and the graph folding of commutative UP-algebra. An

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Hashemi, Ebrahim, Mona Abdi, Abdollah Alhevaz, and Huadong Su. "Domination number of graphs associated with rings." Journal of Algebra and Its Applications 19, no. 01 (2019): 2050009. http://dx.doi.org/10.1142/s0219498820500097.

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The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. Let [Formula: see text] be an associative (not necessarily commutative) ring. We focus on the domination number of the zero-divisor graph [Formula: see text], the compressed zero-divisor graph [Formula: see text] and the unit graph [Formula: see text]. We find some relations between the domination number of the zero-divisor graph and that of the compressed zero-divisor graph. Moreover, some relations between the domination number of [Formula: s

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Joardar, Soumalya, and Arnab Mandal. "Quantum symmetry of graph C∗-algebras associated with connected graphs." Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, no. 03 (2018): 1850019. http://dx.doi.org/10.1142/s0219025718500194.

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We define a notion of quantum automorphism groups of graph [Formula: see text]-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of the underlying directed graph in the sense of Banica [Quantum automorphism groups of homogeneous graphs, J. Funct. Anal. 224 (2005) 243–280] (which is also the symmetry object in the sense of [S. Schmidt and M. Weber, Quantum symmetry of graph [Formula: see text]-algebras, arXiv:1706.08833 ] is shown to be a quantum subgroup of quantum automorphism group in

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6

BARATI, Z., K. KHASHYARMANESH, F. MOHAMMADI, and KH NAFAR. "ON THE ASSOCIATED GRAPHS TO A COMMUTATIVE RING." Journal of Algebra and Its Applications 11, no. 02 (2012): 1250037. http://dx.doi.org/10.1142/s0219498811005610.

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Let R be a commutative ring with nonzero identity. For an arbitrary multiplicatively closed subset S of R, we associate a simple graph denoted by ΓS(R) with all elements of R as vertices, and two distinct vertices x, y ∈ R are adjacent if and only if x+y ∈ S. Two well-known graphs of this type are the total graph and the unit graph. In this paper, we study some basic properties of ΓS(R). Moreover, we will improve and generalize some results for the total and the unit graphs.

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7

DeTemple, Duane, and Jack M. Robertson. "Graphs associated with triangulations of lattice polygons." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 47, no. 3 (1989): 391–98. http://dx.doi.org/10.1017/s1446788700033115.

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AbstractTwo graphs, the edge crossing graph E and the triangle graph T are associated with a simple lattice polygon. The maximal independent sets of vertices of E and T are derived including a formula for the size of the fundamental triangles. Properties of E and T are derived including a formula for the size of the maximal independent sets in E and T. It is shown that T is a factor graph of edge-disjoint 4-cycles, which gives corresponding geometric information, and is a partition graph as recently defined by the authors and F. Harary.

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8

Varghese, Melvin, and G. Sheeja. "On the Cayley type graph construction and characterization associated with ternary semigroups." Journal of Discrete Mathematical Sciences and Cryptography 28, no. 1 (2025): 281–302. https://doi.org/10.47974/jdmsc-2231.

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Cayley graphs of binary semigroup was introduced by Bohdan Zelinka. We introduce two Cayley type graph construction from ternary semigroups. The graph of first kind h (T,B) is a oriented hypergraph and the graph of second kind ( , ) d  T B is a oriented multigraph for a semigroup T with ternary operation and a connection set B ⊆ T. We study subgraphs of these graphs and investigate some properties of these graphs. We give characterization theorems for graphs which are first kind and second kind for a ternary semigroup T.

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Alashwali, Hanaa, and Anwar Saleh. "Common Neighborhood Energy of the Non-Commuting Graphs and Commuting Graphs Associated with Dihedral and Generalized Quaternion Groups." Mathematics 13, no. 11 (2025): 1834. https://doi.org/10.3390/math13111834.

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This paper explores the common neighborhood energy (ECN(Γ)) of graphs derived from the dihedral group D2n and generalized quaternion group Q4n, specifically the non-commuting graph (NCM-graph) and the commuting graph (CM-graph). Studying graphs associated with groups offers a powerful approach to translating algebraic properties into combinatorial structures, enabling the application of graph-theoretic tools to understand group behavior. The common neighborhood energy, defined as the sum of the absolute values of the eigenvalues of the common neighborhood (CN) matrix, i.e., ∑i=1p|ζi|, where {ζ

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Hoppen, Carlos, Yoshiharu Kohayakawa, Richard Lang, Hanno Lefmann, and Henrique Stagni. "Estimating parameters associated with monotone properties." Combinatorics, Probability and Computing 29, no. 4 (2020): 616–32. http://dx.doi.org/10.1017/s0963548320000048.

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AbstractThere has been substantial interest in estimating the value of a graph parameter, i.e. of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the input. Graph parameters that may be successfully estimated in this way are said to be testable or estimable, and the sample complexity qz = qz(ε) of an estimable parameter z is the size of a random sample of a graph G required to ensure that the value of z(G) may be estimated within an error of ε with probability at least 2/3. In this paper, for any f

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11

Lipkovski, Aleksandar. "Digraphs associated with finite rings." Publications de l'Institut Math?matique (Belgrade) 92, no. 106 (2012): 35–41. http://dx.doi.org/10.2298/pim1206035l.

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Let A be a finite commutative ring with unity (ring for short). Define a mapping ? : A2 ? A2 by (a, b) 7? (a + b, ab). One can interpret this mapping as a finite directed graph (digraph) G = G(A) with vertices A2 and arrows defined by ?. The main idea is to connect ring properties of A to graph properties of G. Particularly interesting are rings A = Z/nZ. Their graphs should reflect number-theoretic properties of integers. The first few graphs Gn = G(Z/nZ) are drawn and their numerical parameters calculated. From this list, some interesting properties concerning degrees of vertices and presenc

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12

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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Rehman, Masood Ur, Muhammad Salman, Sheraz Khan, Ayse Dilek Maden, and Faisal Ali. "Mostar index of graphs associated to groups." Main Group Metal Chemistry 45, no. 1 (2022): 124–35. http://dx.doi.org/10.1515/mgmc-2022-0015.

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Abstract A bond-additive connectivity index, named as the Mostar index, is used to measure the amount of peripheral edges of a simple connected graph, where a peripheral edge in a graph is an edge whose one end vertex has more number of vertices closer as compared to the other end vertex. In this study, we count the contribution of peripheral edges in commuting, non-commuting, and non-conjugate graphs associated to the dihedral and semi-dihedral groups. In fact, we compute the Mostar index of these graphs.

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14

Rehman, Shafiq Ur, Ghulam Farid, Tayaba Tariq, and Ebenezer Bonyah. "Equal-Square Graphs Associated with Finite Groups." Journal of Mathematics 2022 (February 24, 2022): 1–6. http://dx.doi.org/10.1155/2022/9244325.

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The graphical representation of finite groups is studied in this paper. For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices x and y are adjacent iff x 2 = y 2 . We call this graph an equal-square graph of the finite group G , symbolized by E S G . Some interesting properties of E S G are studied. Moreover, examples of equal-square graphs of finite cyclic groups, groups of plane symmetries of regular polygons, group of units U n , and the finite abelian groups are constructed.

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15

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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16

D., Parks Allen. "Observations Concerning Chordal Graph Polynomials." International Journal of Sciences Volume 4, no. 2015-01 (2015): 36–39. https://doi.org/10.5281/zenodo.3348831.

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For every graph that is clique equivalent to a connected chordal graph, it is shown that the associated dependence polynomial has a unit root and that the associated clique and independence polynomials have negative unit roots. The dependence polynomial for a graph that is the join of two graphs is also shown to have a unit root when at least one of the two joined graphs is clique equivalent to a connected chordal graph. A condition satisfied by the eigenvalues of graphs that are clique equivalent to connected chordal graphs with clique numbers less than four is identified.Read Complete Articl

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17

Akbari, B., Mark L. Lewis, J. Mirzajani, and A. R. Moghaddamfar. "The solubility graph associated with a finite group." International Journal of Algebra and Computation 30, no. 08 (2020): 1555–64. http://dx.doi.org/10.1142/s0218196720500538.

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The solubility graph associated with a finite group [Formula: see text] is a simple graph whose vertices are the elements of [Formula: see text], and there is an edge between two distinct elements [Formula: see text] and [Formula: see text] if and only if [Formula: see text] is a soluble subgroup of [Formula: see text]. We examine some properties of solubility graphs.

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18

Ding, Junmei, Peng Qian, Jing Ma, Zhiqiang Wang, Yueming Lu, and Xiaqing Xie. "Detect Insider Threat with Associated Session Graph." Electronics 13, no. 24 (2024): 4885. https://doi.org/10.3390/electronics13244885.

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Insider threats pose significant risks to organizational security, often leading to severe data breaches and operational disruptions. While foundational, traditional detection methods suffer from limitations such as labor-intensive rule creation, lack of scalability, and vulnerability to evasion by sophisticated attackers. Recent advancements in graph-based approaches have shown promise by leveraging behavior analysis for threat detection. However, existing methods frequently oversimplify session behaviors and fail to extract fine-grained features, which are critical for identifying subtle mal

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Zhang, Xiujun, Muhammed Nadeem, Sarfraz Ahmad, and Muhammad Kamran Siddiqui. "On applications of bipartite graph associated with algebraic structures." Open Mathematics 18, no. 1 (2020): 57–66. http://dx.doi.org/10.1515/math-2020-0003.

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Abstract The latest developments in algebra and graph theory allow us to ask a natural question, what is the application in real world of this graph associated with some mathematical system? Groups can be used to construct new non-associative algebraic structures, loops. Graph theory plays an important role in various fields through edge labeling. In this paper, we shall discuss some applications of bipartite graphs, related with Latin squares of Wilson loops, such as metabolic pathways, chemical reaction networks, routing and wavelength assignment problem, missile guidance, astronomy and x-ra

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20

MATSUMOTO, KENGO. "FACTOR MAPS OF LAMBDA-GRAPH SYSTEMS AND INCLUSIONS OF C*-ALGEBRAS." International Journal of Mathematics 15, no. 04 (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

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21

Sarathy, R., and J. Ravi Sankar. "Laplacian energy and color based energy for graphs associated with commutative rings." Journal of Discrete Mathematical Sciences and Cryptography 27, no. 8 (2024): 2517–31. https://doi.org/10.47974/jdmsc-2016.

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Let’s assume that ℛ is a commutative ring and its prime graph is PG(ℛ). The vertices of this graph represent elements in ℛ, and an edge connects two different vertices (xa, yb) if and only if xa . yb = 0 or yb . xa = 0. The commutative ring R’s prime digraph is a straightforward graph whose vertices stand in for the equivalence classes of its members, where α ≡ β when anh(α) = anh(β). These equivalence classes are denoted by α–, where ≤ is defined such that α ≤ β when anh(α) ⸦ anh(β), and < on the equivalence classes such that α < β when anh(α) ⸦ anh(β). An arc from β to α exists if α &g

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22

Mudaber, Mohammad Hassan, Nor Haniza Sarmin, and Ibrahim Gambo. "PERFECT CODES IN INDUCED SUBGRAPH OF UNIT GRAPH ASSOCIATED WITH SOME COMMUTATIVE RINGS." Jurnal Teknologi 84, no. 5 (2022): 131–36. http://dx.doi.org/10.11113/jurnalteknologi.v84.17982.

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The unit graph associated with a ring is the graph whose vertices are elements of , and two different vertices and are adjacent if and only if where is the set of unit elements of The aim of this paper is to present the perfect codes in induced subgraph of unit graph associated with some commutative rings with unity in which its vertex set is We characterize some families of commutative rings with induced subgraphs of unit graphs accepting the non-trivial perfect codes, and some other families of commutative rings with induced subgraphs of unit graphs which do not accept perfect codes.

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Monikandan, S., and S. Sundar Raj. "Adversary degree associated reconstruction number of graphs." Discrete Mathematics, Algorithms and Applications 07, no. 01 (2015): 1450069. http://dx.doi.org/10.1142/s1793830914500694.

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A vertex-deleted subgraph of a graph G is called a card of G. A card of G with which the degree of the deleted vertex is also given is called a degree associated card or dacard of G. The adversary degree associated reconstruction number of a graph G, adrn (G), is the minimum number k such that every collection of k dacards of G uniquely determines G. We prove that adrn (G) = 1 + min {t+1, m-t} or 1 + min {t, m - t + 2} for a graph G obtained by subdividing t edges of K1, m. We also prove that if G is a nonempty disconnected graph whose components are cycles or complete graphs, then adrn (G) is

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Abdelkarim, Heba Adel, Eman Rawshdeh, and Edris Rawashdeh. "The Eigensharp Property for Unit Graphs Associated with Some Finite Rings." Axioms 11, no. 7 (2022): 349. http://dx.doi.org/10.3390/axioms11070349.

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Let R be a commutative ring with unity. The unit graph G(R) is defined such that the vertex set of G(R) is the set of all elements of R, and two distinct vertices are adjacent if their sum is a unit in R. In this paper, we show that for each prime, p,G(Zp) and G(Z2p) are eigensharp graphs. Likewise, we show that the unit graph associated with the ring Zp[x]∕x2 is an eigensharp graph.

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Madhumitha, S., and Sudev Naduvath. "Coloring of n-Inordinate Invariant Intersection Graphs." Journal of Combinatorial Mathematics and Combinatorial Computing 123, no. 1 (2024): 369–81. https://doi.org/10.61091/jcmcc123-26.

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In the literature of algebraic graph theory, an algebraic intersection graph called the invariant intersection graph of a graph has been constructed from the automorphism group of a graph. A specific class of these invariant intersection graphs was identified as the n-inordinate invariant intersection graphs, and its structural properties has been studied. In this article, we study the different types of proper vertex coloring schemes of these n-inordinate invariant intersection graphs and their complements, by obtaining the coloring pattern and the chromatic number associated.

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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 (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

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Ali, U., S. A. Bokhary, K. Wahid, and G. Abbas. "On resolvability of a graph associated to a finite vector space." Journal of Algebra and Its Applications 18, no. 02 (2019): 1950029. http://dx.doi.org/10.1142/s0219498819500294.

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In this paper, the resolving parameters such as metric dimension and partition dimension for the nonzero component graph, associated to a finite vector space, are discussed. The exact values of these parameters are determined. It is derived that the notions of metric dimension and locating-domination number coincide in the graph. Independent sets, introduced by Boutin [Determining sets, resolving set, and the exchange property, Graphs Combin. 25 (2009) 789–806], are studied in the graph. It is shown that the exchange property holds in the graph for minimal resolving sets with some exceptions.

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Naz, Kiran, Sarfraz Ahmad, and Eihab Bashier. "On Computing Techniques for Sombor Index of Some Graphs." Mathematical Problems in Engineering 2022 (October 10, 2022): 1–13. http://dx.doi.org/10.1155/2022/1329653.

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In all types of topological indicators, degree-based indicators play a major role in chemical graph theory. The topological index is a fixed numeric value associated with graph isomerism. Firstly, in 1972, the concept of degree-based index was developed by Gutman and Trinajstic. These degree-based indices are divided into two ways, namely, degree and connection number. These degree-based graph indices are positive-valued for non-regular graphs and zero for regular graphs. In this article, we discussed the degree-based Sombor, reduced Sombor, and average Sombor indices for wheel graph, gear gra

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Kunduraci, Tugce, Ceren Elmali, and Tamer Ugur. "The di-topological texture graphs." Thermal Science 26, Spec. issue 2 (2022): 515–24. http://dx.doi.org/10.2298/tsci22s2515k.

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In this study, n-point graphs and n-point texture spaces are examined and graphs that we will call Texture Graphs are obtained. In addition, it is shown how a di-topology can be obtained on the given texture space with the help of this graph. It is shown that a di-topological texture space (S,S,?,k) associated with di-graph (S,G) and each di-graph (S,G) with n points associated with a unique di-topology on texture space. With the graph obtained from co-topology, it has been seen that there is alternative information for the solution of many mathematical and non-mathematical problems in terms o

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ABDOLLAHI, A., and A. MOHAMMADI HASSANABADI. "NON-CYCLIC GRAPH ASSOCIATED WITH A GROUP." Journal of Algebra and Its Applications 08, no. 02 (2009): 243–57. http://dx.doi.org/10.1142/s0219498809003321.

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We associate a graph [Formula: see text] to a non locally cyclic group G (called the non-cyclic graph of G) as follows: take G\ Cyc (G) as vertex set, where Cyc (G) = {x ∈ G | 〈x,y〉 is cyclic for all y ∈ G} is called the cyclicizer of G, and join two vertices if they do not generate a cyclic subgroup. For a simple graph Γ, w(Γ) denotes the clique number of Γ, which is the maximum size (if it exists) of a complete subgraph of Γ. In this paper we characterize groups whose non-cyclic graphs have clique numbers at most 4. We prove that a non-cyclic group G is solvable whenever [Formula: see text]

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Prajapati, Udayan, and Kishan Vyas. "Nourishing Number of Some Associated Graphs." Proyecciones (Antofagasta) 43, no. 1 (2024): 41–51. http://dx.doi.org/10.22199/issn.0717-6279-5541.

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Let N0 = N∪{0} and P(N0) be the power set. An injection f : V (G) → P(N0) is an integer additive set-indexer (IASI) of a graph G if the induced map f+ : E(G) → P(N0) given by f+(uv) = f(u) + f(v) is also an injection, where f(u) + f(v) is the sumset of f(u) and f(v). Moreover, if |f+(uv)| = |f(u)| |f(v)|, for all uv in E(G), then f is a strong IASI of G. The nourishing number of a graph G is the minimum order of the maximal complete subgraph of G such that G admits a strong IASI. In this paper we investigate the admissibility of strong IASI for some associated graphs and calculate their nouris

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Doryn, Dzmitry. "Cohomology of graph hypersurfaces associated to certain Feynman graphs." Communications in Number Theory and Physics 4, no. 2 (2010): 365–415. http://dx.doi.org/10.4310/cntp.2010.v4.n2.a3.

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A. Anu. "Degree Associated Reconstruction Number of Split Graphs with Some Biregular Independent Set." Communications on Applied Nonlinear Analysis 32, no. 8s (2025): 888–92. https://doi.org/10.52783/cana.v32.3881.

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A vertex-deleted subgraph of a graph G with which the degree of the deleted vertex is given is called a degree associated card of G. The degree associated reconstruction number (or drn) of a graph G is the size of the smallest collection of the degree associated cards of G that uniquely determines G. A split graph G is a graph in which the vertices can be partitioned into an independent set and a clique. We prove that the drn is 1 or 2 for all split graphs G of order at least seven in which all the vertices in the independent set have degrees r and s whose distinct degrees differ by at least t

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Ral, Ranelyn I., and Ann Leslie V. Flores. "POWER GRAPH OF B-ALGEBRAS." Advances and Applications in Discrete Mathematics 42, no. 6 (2025): 515–30. https://doi.org/10.17654/0974165825035.

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Power graphs have been extensively studied for their ability to represent algebraic structures through graph-theoretic concepts. This paper investigates the structural properties of power graphs associated with B-algebras, a class of algebras that exhibit certain group-like characteristics. Several graph-theoretic properties, including graph distance measures, are examined. In addition, conditions under which the power graph is complete, Eulerian, or Hamiltonian, as well as the behavior of power graphs under B-homomorphisms, are explored. Finally, the relationship between the center of a B-alg

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Rashid, Mohd, Amal S. Alali, Wasim Ahmed, and Muzibur Rahman Mozumder. "Spectrum of the Cozero-Divisor Graph Associated to Ring Zn." Axioms 12, no. 10 (2023): 957. http://dx.doi.org/10.3390/axioms12100957.

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Let R be a commutative ring with identity 1≠0 and let Z(R)′ be the set of all non-unit and non-zero elements of ring R. Γ′(R) denotes the cozero-divisor graph of R and is an undirected graph with vertex set Z(R)′, w∉zR, and z∉wR if and only if two distinct vertices w and z are adjacent, where qR is the ideal generated by the element q in R. In this article, we investigate the signless Laplacian eigenvalues of the graphs Γ′(Zn). We also show that the cozero-divisor graph Γ′(Zp1p2) is a signless Laplacian integral.

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Larose, Benoit. "Strongly Projective Graphs." Canadian Journal of Mathematics 54, no. 4 (2002): 757–68. http://dx.doi.org/10.4153/cjm-2002-029-7.

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AbstractWe introduce the notion of strongly projective graph, and characterise these graphs in terms of their neighbourhood poset. We describe certain exponential graphs associated to complete graphs and odd cycles. We extend and generalise a result of Greenwell and Lovász [6]: if a connected graph G does not admit a homomorphism to K, where K is an odd cycle or a complete graph on at least 3 vertices, then the graph G × Ks admits, up to automorphisms of K, exactly s homomorphisms to K.

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Volchenkov, Dimitri. "Navigability, Walkability, and Perspicacity Associated with Canonical Ensembles of Walks in Finite Connected Undirected Graphs—Toward Information Graph Theory." Information 14, no. 6 (2023): 338. http://dx.doi.org/10.3390/info14060338.

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Canonical ensembles of walks in a finite connected graph assign the properly normalized probability distributions to all nodes, subgraphs, and nodal subsets of the graph at all time and connectivity scales of the diffusion process. The probabilistic description of graphs allows for introducing the quantitative measures of navigability through the graph, walkability of individual paths, and mutual perspicacity of the different modes of the (diffusion) processes. The application of information theory methods to problems about graphs, in contrast to geometric, combinatoric, algorithmic, and algeb

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Sarmah, Moytri, and Kuntala Patra. "Line graph associated to total graph of idealization." Afrika Matematika 27, no. 3-4 (2015): 485–90. http://dx.doi.org/10.1007/s13370-015-0355-2.

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Hawtin, Daniel R., Cheryl E. Praeger, and Jin-Xin Zhou. "A family of \(2\)-groups and an associated family of semisymmetric, locally \(2\)-arc-transitive graphs." Glasnik Matematicki 58, no. 2 (2023): 259–87. http://dx.doi.org/10.3336/gm.58.2.08.

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A mixed dihedral group is a group \(H\) with two disjoint subgroups \(X\) and \(Y\), each elementary abelian of order \(2^n\), such that \(H\) is generated by \(X\cup Y\), and \(H/H'\cong X\times Y\). In this paper, for each \(n\geq 2\), we construct a mixed dihedral \(2\)-group \(H\) of nilpotency class \(3\) and order \(2^a\) where \(a=(n^3+n^2+4n)/2\), and a corresponding graph \(\Sigma\), which is the clique graph of a Cayley graph of \(H\). We prove that \(\Sigma\) is semisymmetric, that is, \({\mathop{\rm Aut}}(\Sigma)\) acts transitively on the edges but intransitively on the vertices o

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Sharma, Arti, and Atul Gaur. "When the maximal graph is planar, outerplanar, and ring graph." Discrete Mathematics, Algorithms and Applications 10, no. 03 (2018): 1850032. http://dx.doi.org/10.1142/s1793830918500325.

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Let [Formula: see text] be a commutative ring with nonzero identity. Let [Formula: see text] denote the maximal graph associated to [Formula: see text], that is, [Formula: see text] is a graph with vertices as non-units of [Formula: see text], where two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if there is a maximal ideal of [Formula: see text] containing both. In this paper, we characterize the finite commutative rings such that their maximal graph are planar graphs, and we also study the case where they are outerplanar and ring graphs. The equival

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Ejima, Ojonugwa, Abor Isa Garba, and Kazeem Olalekan Aremu. "Subgroup Graphs of Finite Groups." International Journal of Applied Sciences and Smart Technologies 3, no. 2 (2021): 225–40. http://dx.doi.org/10.24071/ijasst.v3i2.3765.

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Let G be a fnite group with the set of subgroups of G denoted by S(G), then the subgroup graphs of G denoted by T(G) is a graph which set of vertices is S(G) such that two vertices H, K in S(G) (H not equal to K)are adjacent if either H is a subgroup of K or K is a subgroup of H. In this paper, we introduce the Subgroup graphs T associated with G. We investigate some algebraic properties and combinatorial structures of Subgroup graph T(G) and obtain that the subgroup graph T(G) of G is never bipartite. Further, we show isomorphism and homomorphism of the Subgroup graphs of finite groups. Let b

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Ahmad, Ali, and S. C. López. "Distance-Based Topological Polynomials Associated with Zero-Divisor Graphs." Mathematical Problems in Engineering 2021 (May 27, 2021): 1–8. http://dx.doi.org/10.1155/2021/4959559.

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Let R be a commutative ring with nonzero identity and let Z R be its set of zero divisors. The zero-divisor graph of R is the graph Γ R with vertex set V Γ R = Z R ∗ , where Z R ∗ = Z R \ 0 , and edge set E Γ R = x , y : x ⋅ y = 0 . One of the basic results for these graphs is that Γ R is connected with diameter less than or equal to 3. In this paper, we obtain a few distance-based topological polynomials and indices of zero-divisor graph when the commutative ring is ℤ p 2 q 2 , namely, the Wiener index, the Hosoya polynomial, and the Shultz and the modified Shultz indices and polynomials.

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Malik, Deny Putra, Muhammad Naoval Husni, Miftahurrahman Miftahurrahman, I. Gede Adhitya Wisnu Wardhana, and Ghazali Semil @ Ismail. "THE CHEMICAL TOPOLOGICAL GRAPH ASSOCIATED WITH THE NILPOTENT GRAPH OF A MODULO RING OF PRIME POWER ORDER." Journal of Fundamental Mathematics and Applications (JFMA) 7, no. 1 (2024): 1–9. http://dx.doi.org/10.14710/jfma.v0i0.20269.

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Chemical topological graph theory constitutes a subdomain within mathematical chemistry that leverages graph theory to model chemical molecules. In this context, a chemical graph serves as a graphical representation of molecular structures. Specifically, a chemical molecule is portrayed as a graph wherein atoms are denoted as vertices, and the interatomic bonds are represented as edges within the graph. Various molecular properties are intricately linked to the topological indices of these molecular graphs. Notably, commonly employed indices encompass the Wiener Index, the Gutman Index, and th

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Koam, Ali N. A., Ali Ahmad, and Azeem Haider. "Radio Number Associated with Zero Divisor Graph." Mathematics 8, no. 12 (2020): 2187. http://dx.doi.org/10.3390/math8122187.

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Radio antennas use different frequency bands of Electromagnetic (EM) Spectrum for switching signals in the forms of radio waves. Regulatory authorities issue a unique number (unique identifying call sign) to each radio center, that must be used in all transmissions. Each radio center propagates channels to the two nearer radio centers so they must use distinctive numbers to avoid interruption. The task of effectively apportioning channels to transmitters is known as the Channel Assignment (CA) problem. CA Problem is discussed under the topic of graph coloring by mathematicians. The radio numbe

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Eshaghian, Mary Mehrnoosh. "MAPPING ARBITRARY HETEROGENEOUS TASK GRAPHS ONTO ARBITRARY HETEROGENEOUS SYSTEM GRAPH." International Journal of Foundations of Computer Science 12, no. 05 (2001): 599–628. http://dx.doi.org/10.1142/s0129054101000680.

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In this paper, a generic technique for mapping arbitrary heterogeneous task graphs onto arbitrary heterogeneous system graphs is presented. The heterogeneous task and system graphs studied in this paper have nonuniform computation and communication weights associated with the nodes and the edges. Two clustering algorithms have been proposed that can be used to obtain a multilayer clustered graph called a Spec graph from a given task graph and a multilayer clustered graph called a Rep graph from a given system graph. We present a mapping algorithm that produces a suboptimal matching of a given

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Hossein-Zadeh, Samaneh, Ali Iranmanesh, Mohammad Ali Hosseinzadeh, and Mark L. Lewis. "On Graphs Associated with Character Degrees and Conjugacy Class Sizes of Direct Products of Finite Groups." Canadian Mathematical Bulletin 58, no. 1 (2015): 105–9. http://dx.doi.org/10.4153/cmb-2014-058-8.

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Abstract.The prime vertex graph, Δ(X), and the common divisor graph, Γ(X), are two graphs that have been deûned on a set of positive integers X. Some properties of these graphs have been studied in the cases where either X is the set of character degrees of a group or X is the set of conjugacy class sizes of a group. In this paper, we gather some results on these graphs arising in the context of direct product of two groups.

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Thomas, Nobin, Lisa Mathew, Sastha Sriram, Atulya K. Nagar, and K. G. Subramanian. "Certain Distance-Based Topological Indices of Parikh Word Representable Graphs." Journal of Mathematics 2021 (May 25, 2021): 1–7. http://dx.doi.org/10.1155/2021/5567663.

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Relating graph structures with words which are finite sequences of symbols, Parikh word representable graphs (PWRGs) were introduced. On the other hand, in chemical graph theory, graphs have been associated with molecular structures. Also, several topological indices have been defined in terms of graph parameters and studied for different classes of graphs. In this study, we derive expressions for computing certain topological indices of PWRGs of binary core words, thereby enriching the study of PWRGs.

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IKEDA, TORU. "SPATIAL GRAPH EXTERIORS REALIZING GIVEN JSJ DECOMPOSITION GRAPHS." Journal of Knot Theory and Its Ramifications 22, no. 05 (2013): 1350020. http://dx.doi.org/10.1142/s021821651350020x.

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If the exterior E(G) of a spatial graph G in a closed orientable 3-manifold is an irreducible 3-manifold with incompressible boundary, there is a unique finite graph Γ associated to the JSJ decomposition of E(G). This paper provides a method for constructing spatial graphs such that a given finite connected graph is associated to the JSJ decompositions of their exteriors.

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Guo, Zhijiang, Yan Zhang, Zhiyang Teng, and Wei Lu. "Densely Connected Graph Convolutional Networks for Graph-to-Sequence Learning." Transactions of the Association for Computational Linguistics 7 (November 2019): 297–312. http://dx.doi.org/10.1162/tacl_a_00269.

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We focus on graph-to-sequence learning, which can be framed as transducing graph structures to sequences for text generation. To capture structural information associated with graphs, we investigate the problem of encoding graphs using graph convolutional networks (GCNs). Unlike various existing approaches where shallow architectures were used for capturing local structural information only, we introduce a dense connection strategy, proposing a novel Densely Connected Graph Convolutional Network (DCGCN). Such a deep architecture is able to integrate both local and non-local features to learn a

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Zeng, Guiling, Muhammad Mobeen Munir, Raheel Farooki, Muhammad Athar, and Jia Bao Liu. "Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis." Journal of Mathematics 2022 (June 6, 2022): 1–8. http://dx.doi.org/10.1155/2022/9706112.

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Graph theory is widely used in power network analysis, complex network, and engineering calculation. Stanley depth is a geometric invariant of the module which is closely related to an algebraic invariant called depth of the module. At first, we propose a generalization of classical gear graph and extended m − level gear graph and then establish general closed formulas for the sharp bounds of Stanley depth of quotient of edge ideals associated to extended m -level gear graph. We establish general closed formulas for the sharp bounds of Stanley depth of quotient of edge ideals associated to ext

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