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Journal articles on the topic 'Complement graphs'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

A.NELLAI MURUGAN, A. NELLAI MURUGAN, and A. ESAKKIMUTHU A.ESAKKIMUTHU. "Domination of Complement of A Splitted Graphs." Indian Journal of Applied Research 4, no. 4 (2011): 392–94. http://dx.doi.org/10.15373/2249555x/apr2014/118.

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2

Giakoumakis, Vassilis, and Jean-Marie Vanherpe. "Bi-complement Reducible Graphs." Advances in Applied Mathematics 18, no. 4 (1997): 389–402. http://dx.doi.org/10.1006/aama.1996.0519.

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3

Yakavi, AL, and Bibi. A. Mydeen. "Generalization of IP Domination Number for Complement Graphs." Indian Journal of Science and Technology 18, no. 12 (2025): 969–73. https://doi.org/10.17485/IJST/v18i12.3959.

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Abstract <strong>Objectives:</strong> This research introduces Isolate Pendant domination parameter, a novel concept applied to complement graphs. <strong>Methods:</strong> This investigation explores Isolate Pendant domination in complement graphs, characterizing the minimum dominating set and satisfying isolate pendant domination conditions within induced graphs, by applying this parameter in −𝐺 to yield insightful results. <strong>Findings:</strong> This study determines the minimum Isolate Pendant Dominating set (IPD-set) in complement graphs, characterizing

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4

Sun, Pak-Kiu. "INCIDENCE COLORING OF REGULAR GRAPHS AND COMPLEMENT GRAPHS." Taiwanese Journal of Mathematics 16, no. 6 (2012): 2289–95. http://dx.doi.org/10.11650/twjm/1500406852.

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5

Kathiresan, K. M., G. Marimuthu, and C. Parameswaran. "The Superior Complement in Graphs." International Journal of Mathematics and Soft Computing 1, no. 1 (2011): 1. http://dx.doi.org/10.26708/ijmsc.2011.1.1.01.

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6

Chartrand, G., S. F. Kapoor, D. R. Lick, and S. Schuster. "The partial complement of graphs." Periodica Mathematica Hungarica 16, no. 2 (1985): 83–95. http://dx.doi.org/10.1007/bf01857589.

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7

Bermudo, Sergio, José M. Rodríguez, José M. Sigarreta, and Eva Tourís. "Hyperbolicity and complement of graphs." Applied Mathematics Letters 24, no. 11 (2011): 1882–87. http://dx.doi.org/10.1016/j.aml.2011.05.011.

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8

Mahato, Iswar, and M. Rajesh Kannan. "Extremal problems for the eccentricity matrices of complements of trees." Electronic Journal of Linear Algebra 39 (June 23, 2023): 339–54. http://dx.doi.org/10.13001/ela.2023.7781.

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The eccentricity matrix of a connected graph $G$, denoted by $\mathcal{E}(G)$, is obtained from the distance matrix of $G$ by keeping the largest nonzero entries in each row and each column and leaving zeros in the remaining ones. The $\mathcal{E}$-eigenvalues of $G$ are the eigenvalues of $\mathcal{E}(G)$. The largest modulus of an eigenvalue is the $\mathcal{E}$-spectral radius of $G$. The $\mathcal{E}$-energy of $G$ is the sum of the absolute values of all $\mathcal{E}$-eigenvalues of $G$. In this article, we study some of the extremal problems for eccentricity matrices of complements of tr

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9

Basavanagoud, B., and Veena Mathad. "Graph Equations for Line Graphs, Jump Graphs, Middle Graphs, Splitting Graphs And Line Splitting Graphs." Mapana - Journal of Sciences 9, no. 2 (2010): 53–61. http://dx.doi.org/10.12723/mjs.17.7.

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For a graph G, let G, L(G), J(G) S(G), L,(G) and M(G) denote Complement, Line graph, Jump graph, Splitting graph, Line splitting graph and Middle graph respectively. In this paper, we solve the graph equations L(G) =S(H), M(G) = S(H), L(G) = LS(H), M(G) =LS(H), J(G) = S(H), M(G) = S(H), J(G) = LS(H) and M(G) = LS(G). The equality symbol '=' stands for on isomorphism between two graphs.

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10

S. Raikar, Vidya, Shailaja S. Shirkol, and Preeti B. Jinagouda. "SECOND ZAGREB INDEX OF k-SPLITTING GRAPH OF GENERALIZED TRANSFORMATION GRAPHS." Journal of Dynamics and Control 9, no. 5 (2025): 57–73. https://doi.org/10.71058/jodac.v9i5006.

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Recently, in [18] Raikar et al. obtained explicit formulae for the first Zagreb index and coindex of k-splitting of generalized transformation graphs and their complement. The aim of this paper is to obtain explicit formulae for the second Zagreb index and coindex of k-splitting of generalized transformation graphs splk(Gab), and followed by this we also obtained analogous expressions for the complements of splk(Gab).

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11

Chellaram Malaravan, A., and A. Wilson Baskar. "A study on distance in graph complement." Discrete Mathematics, Algorithms and Applications 12, no. 03 (2020): 2050045. http://dx.doi.org/10.1142/s1793830920500457.

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The aim of this paper is to determine radius and diameter of graph complements. We provide a necessary and sufficient condition for the complement of a graph to be connected, and determine the components of graph complement. Finally, we completely characterize the class of graphs [Formula: see text] for which the subgraph induced by central (respectively peripheral) vertices of its complement in [Formula: see text] is isomorphic to a complete graph [Formula: see text], for some positive integer [Formula: see text].

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12

Alsharafi, Mohammed, Abdu Alameri, Yusuf Zeren, Mahioub Shubatah, and Anwar Alwardi. "The Y-Index of Some Complement Graph Structures and Their Applications of Nanotubes and Nanotorus." Journal of Mathematics 2024 (January 17, 2024): 1–17. http://dx.doi.org/10.1155/2024/4269325.

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Topological descriptors play a significant role in chemical nanostructures. These topological measures have explicit chemical uses in chemistry, medicine, biology, and computer sciences. This study calculates the Y-index of some graphs and complements graph operations such as join, tensor and Cartesian and strong products, composition, disjunction, and symmetric difference between two simple graphs. Moreover, the Y-polynomial of titania nanotubes and the formulae for the Y-index, Y-polynomial, F-index, F-polynomial, and Y-coindex of the HAC5C7q,p and HAC5C6C7q,p nanotubes and their molecular c

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13

VENKATASUBRAMANIAN, SWAMINATHAN, and RAMAN SUNDARESWARAN. "COMPLEMENTARY FAIR DOMINATION IN GRAPHS." Journal of Science and Arts 23, no. 3 (2023): 765–72. http://dx.doi.org/10.46939/j.sci.arts-23.3-a18.

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In a simple, finite undirected graph G, a dominating set D is a subset of the vertex set V(G) whose closed neighbourhood is V(G). Many types of domination have been studied. The studies are based either on the nature of domination or the type of dominating set or the type of the complement of the dominating set. Interaction between dominating set and its complement is also considered. Fair domination is the domination where every vertex in the complement of a dominating set has equal number of neighbours in the dominating set. In this paper, a dominating set whose vertices have equal number of

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14

Balasubramanian, K. R., and K. Rajeswari. "SOME CONTRIBUTION TO COMPLEMENT OF STRONG NEUTROSOPHIC GRAPHS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 07 (2023): 3607–19. https://doi.org/10.5281/zenodo.8199609.

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The Fundamental operations on Complement of StrongNeutrosophic Graphs. Wehave appliedthe concept  ofstrong  Neutrosophic  Graphsand  also  some  graphs  are  connected,  weexplore  some Particular Cases of strong Neutrosophic Graphs

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15

Al-Masarwah, Anas, and Majdoleen Abu Qamar. "Certain Types of Fuzzy Soft Graphs." New Mathematics and Natural Computation 14, no. 02 (2018): 145–56. http://dx.doi.org/10.1142/s1793005718500102.

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In this paper, we introduce the concepts of uniform vertex fuzzy soft graphs, uniform edge fuzzy soft graphs, degree of a vertex, total degree of a vertex and complement fuzzy soft graphs with some examples. Also, we study regular and totally regular fuzzy soft graphs, and the conditions under which the complement of regular fuzzy soft graph becomes regular as well as totally regular are discussed. Also, we obtain some results related to regular, totally regular and complete fuzzy soft graphs.

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16

Muhiuddin, G., A. M. Alanazi, A. Mahboob, A. H. Alkhaldi, and Wejdan Alatwai. "A Novel Study of Graphs Based on m -Polar Cubic Structures." Journal of Function Spaces 2022 (April 22, 2022): 1–12. http://dx.doi.org/10.1155/2022/2643575.

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By combining the notions of interval-valued m-polar fuzzy graphs and m-polar fuzzy graphs, the notion of m-polar cubic graphs is first introduced. Then, the degree of a vertex in m-polar cubic graphs and complete m-polar cubic graphs is defined. After that, the concepts of direct product and strong product of m-polar cubic graphs are given. Moreover, weak isomorphism and co-weak isomorphism are defined, and examples are given to prove that weak isomorphism and co-weak isomorphism are not an isomorphism. Finally, the notion of complement m-polar cubic graphs and weak complement m-polar cubic gr

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17

EBRAHIMI, MAHDI. "CHARACTER GRAPHS WITH NONBIPARTITE HAMILTONIAN COMPLEMENT." Bulletin of the Australian Mathematical Society 102, no. 1 (2019): 91–95. http://dx.doi.org/10.1017/s0004972719001163.

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For a finite group $G$, let $\unicode[STIX]{x1D6E5}(G)$ denote the character graph built on the set of degrees of the irreducible complex characters of $G$. In this paper, we obtain a necessary and sufficient condition which guarantees that the complement of the character graph $\unicode[STIX]{x1D6E5}(G)$ of a finite group $G$ is a nonbipartite Hamiltonian graph.

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18

Mulas, Raffaella, and Zoran Stanić. "Star complements for ±2 in signed graphs." Special Matrices 10, no. 1 (2022): 258–66. http://dx.doi.org/10.1515/spma-2022-0161.

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Abstract In this article, we investigate connected signed graphs which have a connected star complement for both − 2 -2 and 2 (i.e. simultaneously for the two eigenvalues), where − 2 -2 (resp. 2) is the least (largest) eigenvalue of the adjacency matrix of a signed graph under consideration. We determine all such star complements and their maximal extensions (again, relative to both eigenvalues). As an application, we provide a new proof of the result which identifies all signed graphs that have no eigenvalues other than − 2 -2 and 2.

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19

Kırcalı Gürsoy, Necla Kırcalı. "Graphs of Wajsberg Algebras via Complement Annihilating." Symmetry 15, no. 1 (2023): 121. http://dx.doi.org/10.3390/sym15010121.

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In this paper, W-graph, called the notion of graphs on Wajsberg algebras, is introduced such that the vertices of the graph are the elements of Wajsberg algebra and the edges are the association of two vertices. In addition to this, commutative W-graphs are also symmetric graphs. Moreover, a graph of equivalence classes of Wajsberg algebra is constructed. Meanwhile, new definitions as complement annihilator and ▵-connection operator on Wajsberg algebras are presented. Lemmas and theorems on these notions are proved, and some associated results depending on the graph’s algebraic properties are

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20

AL-Omeri, Wadei Faris AL, M. Kaviyarasu, and Rajeshwari M. "Identifying Internet Streaming Services using Max Product of Complement in Neutrosophic Graphs." International Journal of Neutrosophic Science 23, no. 1 (2024): 257–72. http://dx.doi.org/10.54216/ijns.230123.

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The complement of the highest result of multiplication of two neutrosophic graphs is determined in this study. In the complement of the maximum product of a neutrosophic graph, the degree of a vertex is investigated. The complement of the maximum product of two normal neutrosophic graphs has several results that are presented and proven. Finally, we have offered a neutrosophic graph application for locating an online streaming service using normalized Hamming distance.

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21

Merkel, Owen. "Recolouring weakly chordal graphs and the complement of triangle-free graphs." Discrete Mathematics 345, no. 3 (2022): 112708. http://dx.doi.org/10.1016/j.disc.2021.112708.

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22

Golinskii, L. "Spectra of infinite graphs via Schur complement." Operators and Matrices, no. 2 (2017): 389–96. http://dx.doi.org/10.7153/oam-11-27.

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23

Golinskii, L. "Spectra of infinite graphs via Schur complement." Operators and Matrices, no. 2 (2017): 389–96. http://dx.doi.org/10.7153/oam-2017-11-27.

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24

Kousalya, P., and S. Pachiyammal. "Complement of Interval Valued Intuitionistic Fuzzy Graphs." ScieXplore: International Journal of Research in Science 2, no. 1 (2015): 1. http://dx.doi.org/10.15613/sijrs/2015/v2i1/80078.

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25

Narayan, Sandeep. "Some Remarks on Complement of Fuzzy Graphs." IOSR Journal of Mathematics 7, no. 4 (2013): 75–77. http://dx.doi.org/10.9790/5728-0747577.

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26

Varghese, Renny P., and D. Susha. "Vertex Distance Complement Spectra of Some Graphs." Annals of Pure and Applied Mathematics 16, no. 1 (2018): 69–80. http://dx.doi.org/10.22457/apam.v16n1a9.

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27

Govindan, Vetrivel, Mullai Murugappan, Grienggrai Rajchakit, Surya R, and Subraja Saravanan. "Complement Properties of Pythagorean Co-Neutrosophic Graphs." International Journal on Robotics, Automation and Sciences 6, no. 2 (2024): 42–51. http://dx.doi.org/10.33093/ijoras.2024.6.2.7.

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The origination of graphs with neutrosophic type where membership of indeterminacy expels the vague results, by increasing the accuracy is used to extend application through the graphical environment. Since it is an extension of the intuitionistic type, there comes an immediate need to extend its findings and application to the neutrosophic type. Reversing the conditions of neutrosophic graphs by introducing the anti-behavior properties will produce an adequate number of new results and data, breaking the backlog in approaching decision-making problems and other real-world applications. This r

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28

Milanič, Martin, Anders Sune Pedersen, Daniel Pellicer, and Gabriel Verret. "Graphs whose complement and square are isomorphic." Discrete Mathematics 327 (July 2014): 62–75. http://dx.doi.org/10.1016/j.disc.2014.03.018.

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29

Talebi, Ali Asghar, and Hossein Rashmanlou. "Complement and Isomorphism on Bipolar Fuzzy Graphs." Fuzzy Information and Engineering 6, no. 4 (2014): 505–22. http://dx.doi.org/10.1016/j.fiae.2015.01.007.

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30

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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31

Ratheesh, K. P. "On Soft Graphs and Chained Soft Graphs." International Journal of Fuzzy System Applications 7, no. 2 (2018): 85–102. http://dx.doi.org/10.4018/ijfsa.2018040105.

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Soft set theory has a rich potential for application in many scientific areas such as medical science, engineering and computer science. This theory can deal uncertainties in nature by parametrization process. In this article, the authors explore the concepts of soft relation on a soft set, soft equivalence relation on a soft set, soft graphs using soft relation, vertex chained soft graphs and edge chained soft graphs and investigate various types of operations on soft graphs such as union, join and complement. Also, it is established that every fuzzy graph is an edge chained soft graph.

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32

Elakkiya, A., and M. Yamuna. "Planar Characterization – Graph Domination Graphs." International Journal of Engineering & Technology 7, no. 4.10 (2018): 949. http://dx.doi.org/10.14419/ijet.v7i4.10.26634.

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33

Hamidi, Mohammad, and Florentin Smarandache. "Valued-inverse Dombi neutrosophic graph and application." AIMS Mathematics 8, no. 11 (2023): 26614–31. http://dx.doi.org/10.3934/math.20231361.

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<abstract><p>Utilizing two ideas of neutrosophic subsets (NS) and triangular norms, we introduce a new type of graph as valued-inverse Dombi neutrosophic graphs. The valued-inverse Dombi neutrosophic graphs are a generalization of inverse neutrosophic graphs and are dual to Dombi neutrosophic graphs. We present the concepts of (complete) strong valued-inverse Dombi neutrosophic graphs and analyze the complement of (complete) strong valued-inverse Dombi neutrosophic graphs and self-valued complemented valued-inverse Dombi neutrosophic graphs. Since the valued-inverse Dombi neutrosop

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34

Johns, Garry, and Karen Sleno. "Antipodal graphs and digraphs." International Journal of Mathematics and Mathematical Sciences 16, no. 3 (1993): 579–86. http://dx.doi.org/10.1155/s0161171293000717.

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The antipodal graph of a graphG, denoted byA(G), has the same vertex set asGwith an edge joining verticesuandvifd(u,v)is equal to the diameter ofG. (IfGis disconnected, thendiam G=∞.) This definition is extended to a digraphDwhere the arc(u,v)is included inA(D)ifd(u,v)is the diameter ofD. It is shown that a digraphDis an antipodal digraph if and only ifDis the antipodal digraph of its complement. This generalizes a known characterization for antipodal graphs and provides an improved proof. Examples and properties of antipodal digraphs are given. A digraphDis self-antipodal ifA(D)is isomorphic

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35

Girsh, A. "Intersection Operation on a Complex Plane." Geometry & Graphics 9, no. 1 (2021): 20–28. http://dx.doi.org/10.12737/2308-4898-2021-9-1-20-28.

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Two plane algebraic curves intersect at the actual intersection points of these curves’ graphs. In addition to real intersection points, algebraic curves can also have imaginary intersection points. The total number of curves intersection points is equal to the product of their orders mn. The number of imaginary intersection points can be equal to or part of mn. The position of the actual intersection points is determined by the graphs of the curves, but the imaginary intersection points do not lie on the graphs of these curves, and their position on the plane remains unclear. This work aims t

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36

Ranjith, Athira P., and Joseph Varghese Kureethara. "SUM SIGNED GRAPHS – II." Ural Mathematical Journal 9, no. 1 (2023): 121. http://dx.doi.org/10.15826/umj.2023.1.010.

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In this paper, the study of sum signed graphs is continued. The balancing and switching nature of the graphs are analyzed. The concept of \(rna\) number is revisited and an important relation between the number and its complement is established.

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37

Kovijanic-Vukicevic, Zana, and Vladimir Bozovic. "Bicyclic graphs with minimal values of the detour index." Filomat 26, no. 6 (2012): 1263–72. http://dx.doi.org/10.2298/fil1206263k.

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We are looking for the graphs with minimal detour index in the class of connected bicyclic graphs. For the fixed number of vertices, we split the problem into two cases: bicyclic graphs without common edges between cycles and the complement of it. In both cases, we find graphs with minimal detour index.

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38

Yu, Guidong, Gaixiang Cai, Miaolin Ye, and Jinde Cao. "Energy Conditions for Hamiltonicity of Graphs." Discrete Dynamics in Nature and Society 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/305164.

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LetGbe an undirected simple graph of ordern. LetA(G)be the adjacency matrix ofG, and letμ1(G)≤μ2(G)≤⋯≤μn(G)be its eigenvalues. The energy ofGis defined asℰ(G)=∑i=1n‍|μi(G)|. Denote byGBPTa bipartite graph. In this paper, we establish the sufficient conditions forGhaving a Hamiltonian path or cycle or to be Hamilton-connected in terms of the energy of the complement ofG, and give the sufficient condition forGBPThaving a Hamiltonian cycle in terms of the energy of the quasi-complement ofGBPT.

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39

Amini, Afshin, Babak Amini, and Ehsan Momtahan. "A conception of zero-divisor graph for categories of modules." Journal of Algebra and Its Applications 15, no. 01 (2015): 1650012. http://dx.doi.org/10.1142/s0219498816500122.

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We introduce and study zero-divisor graphs in categories of left modules over a ring R, i.e. R- MOD . The vertices of Γ(R- MOD ) consist of all nonzero morphisms in R- MOD which are not isomorphisms. Two vertices f and g are adjacent if f ◦ g = 0 or g ◦ f = 0. We observe that these graphs are connected and their diameter is equal or less than four. We prove that Γ(R- MOD ) = 3 if and only if R is a right and left perfect ring and R/J(R) is simple artinian. We also characterize all vertices with complements and that when a kernel or a co-kernel can be a complement for a morphism. Some discussio

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40

Girse, Robert D. "Homomorphisms of completen-partite graphs." International Journal of Mathematics and Mathematical Sciences 9, no. 1 (1986): 193–95. http://dx.doi.org/10.1155/s0161171286000224.

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41

Koch, Sebastian. "About Graph Complements." Formalized Mathematics 28, no. 1 (2020): 41–63. http://dx.doi.org/10.2478/forma-2020-0004.

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42

Jawad Abd, Shakir, and Hayder B. Shelash. "The complement subgroup product graph of a cyclic group." Journal of Discrete Mathematical Sciences and Cryptography 28, no. 2 (2025): 393–97. https://doi.org/10.47974/jdmsc-2025.

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In this paper, we introduced a new graph, it is called complement subgroup product graphs (CSPG) derived from cyclic groups. The set of vertices is the proper subgroup of group G and for each two proper subgroups H, K is connected if and only if HK=G. We study the formulas for vertex degrees, isolation properties of certain graphs, matrix degree representations, and edge calculations.

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43

Yulianto, T., N. Hayati, I. H. Agustin, et al. "Properties of cartesian multiplication operations in complete fuzzy graphs, effective fuzzy graphs and complement fuzzy graphs." Journal of Physics: Conference Series 1538 (May 2020): 012022. http://dx.doi.org/10.1088/1742-6596/1538/1/012022.

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44

Mitchell, Lon. "Graph degeneracy and orthogonal vector representations." Electronic Journal of Linear Algebra 39 (May 18, 2023): 282–85. http://dx.doi.org/10.13001/ela.2023.6907.

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45

Khandekar, Nilesh, and Vinayak Joshi. "Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures." Mathematica Slovaca 73, no. 5 (2023): 1099–118. http://dx.doi.org/10.1515/ms-2023-0081.

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ABSTRACT In this paper, we characterize the perfect zero-divisor graphs and chordal zero-divisor graphs (its complement) of ordered sets. These results are applied to the zero-divisor graphs of finite reduced rings, the comaximal ideal graphs of rings, the annihilating ideal graphs of rings, the intersection graphs of ideals of rings, and the intersection graphs of subgroups of groups. In fact, it is shown that these graphs associated with a commutative ring R with identity can be effectively studied via the zero-divisor graph of a specially constructed poset from R.

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46

HARLANDER, JENS, and STEPHAN ROSEBROCK. "GENERALIZED KNOT COMPLEMENTS AND SOME ASPHERICAL RIBBON DISC COMPLEMENTS." Journal of Knot Theory and Its Ramifications 12, no. 07 (2003): 947–62. http://dx.doi.org/10.1142/s0218216503002871.

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We generalize some aspects of standard knot-theory to all ribbon-disc complements. We study asphericity of the complement of properly embedded links in certain contractible singular 3-manifolds that should be thought off as replacements of the 3-ball in the classical setting. We apply our results to show asphericity of 2-complexes modelled on labelled oriented graphs that correspond to alternating prime projections on some surface.

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47

Alsharafi, M., M. Shubatah, and A. Alameri. "THE HYPER-ZAGREB INDEX OF SOME COMPLEMENT GRAPHS." Advances in Mathematics: Scientific Journal 9, no. 6 (2020): 3631–42. http://dx.doi.org/10.37418/amsj.9.6.41.

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48

Jansrang, Monsikarn, and Sivaram K. Narayan. "Graph complement conjecture for classes of shadow graphs." Operators and Matrices, no. 2 (2021): 589–614. http://dx.doi.org/10.7153/oam-2021-15-40.

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49

Palanivel, Naveen, and A. V. Chithra. "Energy and Laplacian energy of unitary addition Cayley graphs." Filomat 33, no. 11 (2019): 3599–613. http://dx.doi.org/10.2298/fil1911599p.

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Abstract:

In this paper, we obtain the eigenvalues and Laplacian eigenvalues of the unitary addition Cayley graph Gn and its complement. Moreover, we compute the bounds for energy and Laplacian energy for Gn and its complement. In addition, we prove that Gn is hyperenergetic if and only if n is odd other than the prime number and power of 3 or n is even and has at least three distinct prime factors. It is also shown that the complement of Gn is hyperenergetic if and only if n has at least two distinct prime factors and n ? 2p.

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A. Anat Jaslin Jini. "Relatively Prime Domination Number in Triangular Snake Graphs." Advances in Nonlinear Variational Inequalities 28, no. 2 (2024): 159–65. http://dx.doi.org/10.52783/anvi.v28.1912.

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Abstract:

A set S⊆V is said to be relatively prime dominating set if it is a dominating set with at least two elements and for every pair of vertices u and v in S, (deg⁡(u),deg⁡〖(v))〗=1 and the minimum cardinality of a relatively prime dominating set is called relatively prime domination number and it is denoted by γ_rpd (G). If there is no such pair exist, then γ_rpd (G)=0. For a finite undirected graph G(V,E) and a subset V, the switching of G by is defined as the graph (V, ) which is obtained from G by removing all edges between and its complement V- and adding as edges all non-edges between and V- .

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