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Journal articles on the topic 'Join of graphs'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Nieminen, Juhani. "Join space graphs." Journal of Geometry 33, no. 1-2 (1988): 99–103. http://dx.doi.org/10.1007/bf01230609.

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2

Lukoťka, Robert, and Edita Rollová. "Flows on the join of two graphs." Mathematica Bohemica 138, no. 4 (2013): 383–96. http://dx.doi.org/10.21136/mb.2013.143511.

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3

Akka, D. G., and J. K. Bano. "Characterization of $2$-minimally nonouterplanar join graphs." Mathematica Bohemica 126, no. 1 (2001): 1–13. http://dx.doi.org/10.21136/mb.2001.133919.

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4

Arriola, Benjier, Shaleema Arriola, Bayah Amiruddin-Rajik, and Sherlyn Sappayani. "Independence-Preserving Operations: Effects in Polynomial Representations." International Journal of Mathematics and Computer Science 20, no. 1 (2024): 49–52. http://dx.doi.org/10.69793/ijmcs/01.2025/bayad.

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In this piece of work, we show that independent sets are preserved in the join operation of graphs. The adjacency property of the join of graphs guarantees a nice representation of the independent neighborhood polynomial of the join of graphs in terms of the independent neighborhood polynomials of graphs being considered.

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5

Hassan, Javier, Anabel E. Gomorez, Ladznar S. Laja, and Eman C. Ahmad. "Formulas and Properties of 2-Hop Domination in Some Graphs." European Journal of Pure and Applied Mathematics 17, no. 2 (2024): 852–59. http://dx.doi.org/10.29020/nybg.ejpam.v17i2.5065.

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In this paper, 2-hop domination parameter is introduced and investigated on some special graphs and on the join of two graphs. Characterizations of 2-hop dominating sets in some special graphs are formulated to derive bounds or formulas of the parameter of these graphs. Moreover, new variant of pointwise non-domination is introduced to characterize 2-hop dominating sets in the join of two graphs. This characterization is used to calculate the exact value of 2-hop domination number of the join of two graphs.

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6

Kwaśnik, Maria, and Danuta Michalak. "The join of graphs and the binding minimality." Časopis pro pěstování matematiky 114, no. 3 (1989): 262–75. http://dx.doi.org/10.21136/cpm.1989.118377.

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7

Dong, Gui Xiang, and Xiu Fang Liu. "Incidence Coloring Number of Some Join Graphs." Applied Mechanics and Materials 602-605 (August 2014): 3185–88. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.3185.

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The incidence coloring of a graph is a mapping from its incidence set to color set in which neighborly incidences are assigned different colors. In this paper, we determined the incidence coloring numbers of some join graphs with paths and paths, cycles, complete graphs, complete bipartite graphs, respectively, and the incidence coloring numbers of some join graphs with complete bipartite graphs and cycles, complete graphs, respectively.

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8

Adame, Luis Enrique, Luis Manuel Rivera, and Ana Laura Trujillo-Negrete. "Hamiltonicity of Token Graphs of Some Join Graphs." Symmetry 13, no. 6 (2021): 1076. http://dx.doi.org/10.3390/sym13061076.

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Let G be a simple graph of order n with vertex set V(G) and edge set E(G), and let k be an integer such that 1≤k≤n−1. The k-token graph G{k} of G is the graph whose vertices are the k-subsets of V(G), where two vertices A and B are adjacent in G{k} whenever their symmetric difference A▵B, defined as (A∖B)∪(B∖A), is a pair {a,b} of adjacent vertices in G. In this paper we study the Hamiltonicity of the k-token graphs of some join graphs. We provide an infinite family of graphs, containing Hamiltonian and non-Hamiltonian graphs, for which their k-token graphs are Hamiltonian. Our result provides

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9

Manju, V. N., T. B. Athul, and G. Suresh Singh. "SOME BOUNDS FOR THE WIENER INDEX OF WEAK JOIN OF TWO GRAPHS." Advances in Mathematics: Scientific Journal 12, no. 1 (2023): 107–13. http://dx.doi.org/10.37418/amsj.12.1.7.

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In 2020, G. Suresh Singh and Manju V. N. \cite{mvn} introduced the concept of weak join of two disjoint graphs with respect to the degrees of the given graphs and categorized them as homogeneous weak join, heterogeneous weak join and studied some of their properties. Homogeneous weak join can be splitted in to three cases namely, odd to odd degree weak join, even to even degree weak join, odd to odd and even to even degree weak join. Similarly, heterogeneous weak join includes the other three cases namely, odd to even degree weak join, even to odd degree weak join, odd to even and even to odd

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10

Dr., S.Nagarajan, G.Kayalvizhi, and G.Priyadharsini. "HF-Index and Y-Index of Some New Graph of Operations." International Journal of Engineering and Advanced Technology (IJEAT) 11, no. 3 (2022): 28–33. https://doi.org/10.35940/ijeat.C3351.0211322.

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In this paper we derive HF index of some graph operations containing join, Cartesian Product, Corona Product of graphs and compute the Y index of new operations of graphs related to the join of graphs

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11

Wu, Bao-Feng, Yuan-Yuan Lou, and Chang-Xiang He. "Signless Laplacian and normalized Laplacian on the H-join operation of graphs." Discrete Mathematics, Algorithms and Applications 06, no. 03 (2014): 1450046. http://dx.doi.org/10.1142/s1793830914500463.

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In this paper, we consider a generalized join operation, that is, the H-join on graphs, where H is an arbitrary graph. In terms of the signless Laplacian and the normalized Laplacian, we determine the spectra of the graphs obtained by this operation on regular graphs. Some additional consequences on the spectral radius, integral graphs and cospectral graphs, etc. are also obtained.

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12

De Simone, Caterina, and C. P. de Mello. "Edge-colouring of join graphs." Theoretical Computer Science 355, no. 3 (2006): 364–70. http://dx.doi.org/10.1016/j.tcs.2005.12.010.

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13

Hell, Pavol, and Pei-Lan Yen. "Join colourings of chordal graphs." Discrete Mathematics 338, no. 12 (2015): 2453–61. http://dx.doi.org/10.1016/j.disc.2015.06.005.

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14

Bača, Martin, Oudone Phanalasy, Joe Ryan, and Andrea Semaničová-Feňovčíková. "Antimagic Labelings of Join Graphs." Mathematics in Computer Science 9, no. 2 (2015): 139–43. http://dx.doi.org/10.1007/s11786-015-0218-0.

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15

Nieminen, Juhani. "Chordal graphs and join spaces." Journal of Geometry 34, no. 1-2 (1989): 146–51. http://dx.doi.org/10.1007/bf01224240.

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16

Machado, Raphael C. S., and Celina M. H. de Figueiredo. "Decompositions for edge-coloring join graphs and cobipartite graphs." Discrete Applied Mathematics 158, no. 12 (2010): 1336–42. http://dx.doi.org/10.1016/j.dam.2009.01.009.

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17

Surya, S. Sarah, and Lian Mathew. "Secure Domination Cover Pebbling Number of Join of graphs." Indian Journal Of Science And Technology 15, no. 27 (2022): 1344–48. http://dx.doi.org/10.17485/ijst/v15i27.2145.

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18

Angeles-Canul, R. J., R. M. Norton, M. C. Opperman, C. C. Paribello, M. C. Russell, and C. Tamon. "Perfect state transfer, integral circulants, and join of graphs." Quantum Information and Computation 10, no. 3&4 (2010): 325–42. http://dx.doi.org/10.26421/qic10.3-4-10.

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We propose new families of graphs which exhibit quantum perfect state transfer. Our constructions are based on the join operator on graphs, its circulant generalizations, and the Cartesian product of graphs. We build upon the results of Ba\v{s}i\'{c} and Petkovi\'{c} ({\em Applied Mathematics Letters} {\bf 22}(10):1609-1615, 2009) and construct new integral circulants and regular graphs with perfect state transfer. More specifically, we show that the integral circulant $\textsc{ICG}_{n}(\{2,n/2^{b}\} \cup Q)$ has perfect state transfer, where $b \in \{1,2\}$, $n$ is a multiple of $16$ and $Q$

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19

HOU, HAILONG, RUI GU, and YOULIN SHANG. "THE JOIN OF SPLIT GRAPHS WHOSE QUASI-STRONG ENDOMORPHISMS FORM A MONOID." Bulletin of the Australian Mathematical Society 91, no. 1 (2014): 1–10. http://dx.doi.org/10.1017/s000497271400046x.

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AbstractIn this paper, we characterise the quasi-strong endomorphisms of the join of split graphs. We give conditions under which the quasi-strong endomorphisms of the join of split graphs form a monoid.

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20

Hou, Hailong, Yanhua Song, and Rui Gu. "The join of split graphs whose completely regular endomorphisms form a monoid." Open Mathematics 15, no. 1 (2017): 833–39. http://dx.doi.org/10.1515/math-2017-0071.

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Abstract In this paper, completely regular endomorphisms of the join of split graphs are investigated. We give conditions under which all completely regular endomorphisms of the join of two split graphs form a monoid.

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21

Alhevaz, Abdollah, Maryam Baghipur, Hilal A. Ganie, and Yilun Shang. "The Generalized Distance Spectrum of the Join of Graphs." Symmetry 12, no. 1 (2020): 169. http://dx.doi.org/10.3390/sym12010169.

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Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D ( G ) and diagonal matrix of the vertex transmissions T r ( G ) . We determine the spectrum of the join of two graphs and of the join of a regular graph with another graph, which is the union of two different regular graphs. Moreover, thanks to the symmetry of the matrices involved, we study the generalized distance spectrum of the graphs obtained by generalization of the join graph operation through their eig

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22

Manjunatha, B. J., B. R. Rakshith, K. N. Prakasha, and N. V. Sayinath Udupa. "Distance Spectra of Some Double Join Operations of Graphs." International Journal of Mathematics and Mathematical Sciences 2024 (May 27, 2024): 1–8. http://dx.doi.org/10.1155/2024/2017748.

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In literature, several types of join operations of two graphs based on subdivision graph, Q-graph, R-graph, and total graph have been introduced, and their spectral properties have been studied. In this paper, we introduce a new double join operation based on H1,H2-merged subdivision graph. We compute the spectrum of a special block matrix and then use it to describe the distance spectra of some double join operations of graphs. At last, we give several families of distance equienergetic graphs of diameter 3.

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23

Ahmed, Haifa, and Mohammed Alsharafi. "Domination on Bipolar Fuzzy Graph Operations: Principles, Proofs, and Examples." Neutrosophic Systems with Applications 17 (May 2, 2024): 34–46. http://dx.doi.org/10.61356/j.nswa.2024.17245.

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Bipolar fuzzy graphs, capable of capturing situations with both positive and negative memberships, have found diverse applications in various disciplines, including decision-making, computer science, and social network analysis. This study investigates the domain of domination and global domination numbers within bipolar fuzzy graphs, owing to their relevance in these aforementioned practical fields. In this study, we introduce certain operations on bipolar fuzzy graphs, such as intersection, join, and union of two graphs. Furthermore, we analyze the domination number and the global domination

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24

T K, Jahfar, and Chithra A V. "Central vertex join and central edge join of two graphs." AIMS Mathematics 5, no. 6 (2020): 7214–33. http://dx.doi.org/10.3934/math.2020461.

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25

Xu, Shaohan, and Kexiang Xu. "Resistance distances in generalized join graphs." Discrete Applied Mathematics 362 (February 2025): 18–33. http://dx.doi.org/10.1016/j.dam.2024.11.013.

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26

Bandelt, Hans-Jürgen, and Henry Martyn Mulder. "Pseudo-median graphs are join spaces." Discrete Mathematics 109, no. 1-3 (1992): 13–26. http://dx.doi.org/10.1016/0012-365x(92)90275-k.

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27

Pokorný, M., and P. Híc. "DISTANCE SPECTRA OF H-JOIN GRAPHS." Advances and Applications in Discrete Mathematics 17, no. 3 (2016): 305–21. http://dx.doi.org/10.17654/dm017030305.

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28

Silveira, Luciano L., and Marcelo H. de Carvalho. "Ear decompositions of join covered graphs." Electronic Notes in Discrete Mathematics 37 (August 2011): 171–76. http://dx.doi.org/10.1016/j.endm.2011.05.030.

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29

Georgiadis, Loukas, Stavros D. Nikolopoulos, and Leonidas Palios. "Join-Reachability Problems in Directed Graphs." Theory of Computing Systems 55, no. 2 (2013): 347–79. http://dx.doi.org/10.1007/s00224-013-9450-7.

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30

Sebő, András. "Finding thet-join structure of graphs." Mathematical Programming 36, no. 2 (1986): 123–34. http://dx.doi.org/10.1007/bf02592020.

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31

Wang, Tao, Ming Ju Liu, and De Ming Li. "A class of antimagic join graphs." Acta Mathematica Sinica, English Series 29, no. 5 (2012): 1019–26. http://dx.doi.org/10.1007/s10114-012-1559-0.

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32

de Carvalho, Marcelo H., and C. H. C. Little. "Circuit decompositions of join-covered graphs." Journal of Graph Theory 62, no. 3 (2009): 220–33. http://dx.doi.org/10.1002/jgt.20400.

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33

Gayathri, M., та R. Rajkumar. "Spectra of (M,ℳ)-corona-join of graphs". Proyecciones (Antofagasta) 42, № 1 (2023): 105–24. http://dx.doi.org/10.22199/issn.0717-6279-5454.

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In this paper, we introduce the (M, ℳ)-corona-join of G and ℋk constrained by vertex subsets 𝒯, which is the union of two graphs: one is the M-generalized corona of a graph G and a family of graphs ℋk constrained by vertex subset 𝒯 of the graphs in ℋk, where M is a suitable matrix; and the other one is the ℳ -join of ℋk, where ℳ is a collection of matrices. We determine the spectra of the adjacency, the Laplacian, the signless Laplacian and the normalized Laplacian matrices of some special cases of the (M, ℳ)-corona-join of G and ℋk constrained by vertex subsets 𝒯. These results enable us to d

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34

Kaliyaperumal, Sakthidevi, and Kalyani Desikan. "Universal Distance Spectra of Join of Graphs." European Journal of Pure and Applied Mathematics 17, no. 1 (2024): 462–76. http://dx.doi.org/10.29020/nybg.ejpam.v17i1.5019.

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Consider G a simple connected graph. In this paper, we introduce the Universal distance matrix UD (G). For α, β, γ, δ ∈ R and β ̸= 0, the universal distance matrix UD (G) is defined asUD (G) = αTr (G) + βD(G) + γJ + δI,where Tr (G) is the diagonal matrix whose elements are the vertex transmissions, and D(G) is the distance matrix of G. Here J is the all-ones matrix, and I is the identity matrix. In this paper, we obtain the universal distance spectra of regular graph, join of two regular graphs, joined union of three regular graphs, generalized joined union of n disjoint graphs with one arbitr

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35

Fortes, Jana, and Michal Staš. "Crossing Numbers of Join Product with Discrete Graphs: A Study on 6-Vertex Graphs." Mathematics 11, no. 13 (2023): 2960. http://dx.doi.org/10.3390/math11132960.

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Reducing the number of crossings on graph edges can be useful in various applications, including network visualization, circuit design, graph theory, cartography or social choice theory. This paper aims to determine the crossing number of the join product G*+Dn, where G* is a connected graph isomorphic to K2,2,2∖{e1,e2} obtained by removing two edges e1,e2 with a common vertex and a second vertex from the different partitions of the complete tripartite graph K2,2,2, and Dn is a discrete graph composed of n isolated vertices. The proofs utilize known exact crossing number values for join produc

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36

Asghar, Syed Sheraz, Muhammad Ahsan Binyamin, Yu-Ming Chu, Shehnaz Akhtar, and Mehar Ali Malik. "Szeged-type indices of subdivision vertex-edge join (SVE-join)." Main Group Metal Chemistry 44, no. 1 (2021): 82–91. http://dx.doi.org/10.1515/mgmc-2021-0011.

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Abstract In this article, we compute the vertex Padmakar-Ivan (PIv ) index, vertex Szeged (Szv ) index, edge Padmakar-Ivan (PIe ) index, edge Szeged (Sze ) index, weighted vertex Padmakar-Ivan (wPIv ) index, and weighted vertex Szeged (wSzv ) index of a graph product called subdivision vertex-edge join of graphs.

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37

Susada, Bryan L., and Rolito G. Eballe. "Independent Semitotal Domination in the Join of Graphs." Asian Research Journal of Mathematics 19, no. 3 (2023): 25–31. http://dx.doi.org/10.9734/arjom/2023/v19i3647.

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A subset W \(\subseteq\) V (G) of a graph G is an independent semitotal dominating set of G, abbreviated ISTd-set of G, if W is an independent dominating set of G and every element of W is exactly of distance 2 from at least one other element of W. The independent semitotal domination number of G, denoted by \(\gamma\)it2(G), is the minimum cardinality of an ISTd-set of G. In this paper, we study the concept of independent semitotal domination in graphs and investigate the conditions for graphs on which the ISTd-sets exist. Further, the ISTd-sets of the join of any two graphs are examined. Con

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38

Zhou, Ting, Zhen Lin, and Lianying Miao. "A note on marginal entropy of graphs." Open Journal of Discrete Applied Mathematics 5, no. 1 (2022): 59–68. http://dx.doi.org/10.30538/psrp-odam2022.0071.

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In 2006, Konstantinova proposed the marginal entropy of a graph based on the Wiener index. In this paper, we obtain the marginal entropy of the complete multipartite graphs, firefly graphs, lollipop graphs, clique-chain graphs, Cartesian product and join of two graphs, which extends the results of Sahin.

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39

M., Durga, and Dr.S.Nagarajan. "TWO TOPOLOGICAL INDICES OF TWO NEW VARIANTS OF GRAPH PRODUCTS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 08 (2023): 3704–7. https://doi.org/10.5281/zenodo.8300477.

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Graph operations are essential to developing advanced network structures from simple graphs. In [12] they defined two new variants of corona product and discovered their topological indices. In this Study, we extended the work and obtain the formulas of Y- Index and Redefined third Zagreb index for corona join product and Sub-division vertex join product of graphs

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40

Seidy, Essam EI, Salah ElDin Hussein, and Atef Abo Elkher. "Spectra of some Operations on Graphs." JOURNAL OF ADVANCES IN MATHEMATICS 11, no. 9 (2016): 5654–60. http://dx.doi.org/10.24297/jam.v11i9.828.

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In this paper, we consider a finite undirected and connected simple graph G(E, V) with vertex set V(G) and edge set E(G).We introduced a new computes the spectra of some operations on simple graphs [union of disjoint graphs, join of graphs, cartesian product of graphs, strong cartesian product of graphs, direct product of graphs].

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41

Uma, L., and G. Rajasekaran. "The vertex local antimagicness for Knödel and Fibonacci graphs." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 35, no. 2 (2025): 297–314. https://doi.org/10.35634/vm250209.

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In this article, we present the vertex local anti-magic chromatic number for some Knödel graphs $\mathcal{G}$ and Fibonacci graphs; disjoint union of Knödel graphs; and the join graphs $\mathcal{G}\vee \mathcal{H}$, where ${\mathcal{H}\in\{O_s,K_s,C_s,K_{s,\ell}\}}$.

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42

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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43

Armada, Cris Laquibla, and Sergio, Jr R. Canoy. "Forcing Independent Domination Number of a Graph." European Journal of Pure and Applied Mathematics 12, no. 4 (2019): 1371–81. http://dx.doi.org/10.29020/nybg.ejpam.v12i4.3484.

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In this paper, we obtain the forcing independent domination number of some special graphs. Further, we determine the forcing independent domination number of graphs under some binary operations such join, corona and lexicographic product of two graphs.

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44

ANGELES-CANUL, RICARDO JAVIER, RACHAEL M. NORTON, MICHAEL C. OPPERMAN, CHRISTOPHER C. PARIBELLO, MATTHEW C. RUSSELL, and CHRISTINO TAMON. "QUANTUM PERFECT STATE TRANSFER ON WEIGHTED JOIN GRAPHS." International Journal of Quantum Information 07, no. 08 (2009): 1429–45. http://dx.doi.org/10.1142/s0219749909006103.

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This paper studies quantum perfect state transfer on weighted graphs. We prove that the join of a weighted two-vertex graph with any regular graph has perfect state transfer. This generalizes a result of Casaccino et al.1 where the regular graph is a complete graph with or without a missing edge. In contrast, we prove that the half-join of a weighted two-vertex graph with any weighted regular graph has no perfect state transfer. As a corollary, unlike for complete graphs, adding weights in complete bipartite graphs does not produce perfect state transfer. We also observe that any Hamming graph

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45

Chen, Haiyan, and Yu Chen. "Bartholdi Zeta Functions of Generalized Join Graphs." Graphs and Combinatorics 34, no. 1 (2017): 207–22. http://dx.doi.org/10.1007/s00373-017-1867-3.

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46

Krepkiy, I. A. "Sandpile Groups and the Join of Graphs." Journal of Mathematical Sciences 196, no. 2 (2014): 184–86. http://dx.doi.org/10.1007/s10958-013-1650-9.

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47

Klešč, Marián. "The Join of Graphs and Crossing Numbers." Electronic Notes in Discrete Mathematics 28 (March 2007): 349–55. http://dx.doi.org/10.1016/j.endm.2007.01.049.

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48

Koh, K. M., L. Y. Phoon, and K. W. Soh. "The Gracefulness of the Join of Graphs." Electronic Notes in Discrete Mathematics 48 (July 2015): 57–64. http://dx.doi.org/10.1016/j.endm.2015.05.009.

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49

Wang, Tao, and Deming Li. "A new class of antimagic join graphs." Wuhan University Journal of Natural Sciences 19, no. 2 (2014): 153–55. http://dx.doi.org/10.1007/s11859-014-0993-5.

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50

Paluga, Rolando N. "Monophonic Polynomial of the Join of Graphs." Journal of the Indonesian Mathematical Society 31, no. 1 (2025): 1686. https://doi.org/10.22342/jims.v31i1.1686.

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The monophonic polynomial of a graph $G$, denoted by $M(G,x)$, is the polynomial $M(G,x) = \sum_{k=m(G)}^{|G|}M(G, k)x^k $, where $|G|$ is the order of $G$ and $M(G, k)$ is the number of monophonic sets in $G$ with cardinality $k$. In this paper, we delve into some characterizations of monophonic sets in the join of two graphs and use it to determine its corresponding monophonic polynomial. Moreover, we also present the monophonic polynomials of the complete graph $K_n$ $(n \geq 1)$, the path $P_n$ $(n \geq 3)$, the cycle $C_n$ $(n \geq 4)$, the fan $F_n$ $(n \geq 3)$, the wheel $W_n$ $(n \geq

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