• Title/Summary/Keyword: s-regular graphs

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CUBIC SYMMETRIC GRAPHS OF ORDER 10p3

  • Ghasemi, Mohsen
    • Journal of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.241-257
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    • 2013
  • An automorphism group of a graph is said to be $s$-regular if it acts regularly on the set of $s$-arcs in the graph. A graph is $s$-regular if its full automorphism group is $s$-regular. In the present paper, all $s$-regular cubic graphs of order $10p^3$ are classified for each $s{\geq}1$ and each prime $p$.

CUBIC s-REGULAR GRAPHS OF ORDER 12p, 36p, 44p, 52p, 66p, 68p AND 76p

  • Oh, Ju-Mok
    • Journal of applied mathematics & informatics
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    • v.31 no.5_6
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    • pp.651-659
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    • 2013
  • A graph is $s$-regular if its automorphism group acts regularly on the set of its $s$-arcs. In this paper, the cubic $s$-regular graphs of order 12p, 36p, 44p, 52p, 66p, 68p and 76p are classified for each $s{\geq}1$ and each prime $p$. The number of cubic $s$-regular graphs of order 12p, 36p, 44p, 52p, 66p, 68p and 76p is 4, 3, 7, 8, 1, 4 and 1, respectively. As a partial result, we determine all cubic $s$-regular graphs of order 70p except for $p$ = 31, 41.

The Gallai and Anti-Gallai Graphs of Strongly Regular Graphs

  • Jeepamol J. Palathingal;Aparna Lakshmanan S.;Greg Markowsky
    • Kyungpook Mathematical Journal
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    • v.64 no.1
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    • pp.171-184
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    • 2024
  • In this paper, we show that if G is strongly regular then the Gallai graph Γ(G) and the anti-Gallai graph ∆(G) of G are edge-regular. We also identify conditions under which the Gallai and anti-Gallai graphs are themselves strongly regular, as well as conditions under which they are 2-connected. We include also a number of concrete examples and a discussion of spectral properties of the Gallai and anti-Gallai graphs.

SUPER VERTEX MEAN GRAPHS OF ORDER ≤ 7

  • LOURDUSAMY, A.;GEORGE, SHERRY
    • Journal of applied mathematics & informatics
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    • v.35 no.5_6
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    • pp.565-586
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    • 2017
  • In this paper we continue to investigate the Super Vertex Mean behaviour of all graphs up to order 5 and all regular graphs up to order 7. Let G(V,E) be a graph with p vertices and q edges. Let f be an injection from E to the set {1,2,3,${\cdots}$,p+q} that induces for each vertex v the label defined by the rule $f^v(v)=Round\;\left({\frac{{\Sigma}_{e{\in}E_v}\;f(e)}{d(v)}}\right)$, where $E_v$ denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1,2,3,${\cdots}$,p+q}. Such an injective function f is called a super vertex mean labeling of a graph G and G is called a Super Vertex Mean Graph.

ON THE GENUS OF Sm × Sn

  • Cristofori, Paola
    • Journal of the Korean Mathematical Society
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    • v.41 no.3
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    • pp.407-421
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    • 2004
  • By using a recursive algorithm, we construct edge-coloured graphs representing products of spheres and consequently we give upper bounds for the regular genus of ${\mathbb{S}}^{m}\;\times\;{\mathbb{S}}^{n}$, for each m, n > 0.

On the Seidel Laplacian and Seidel Signless Laplacian Polynomials of Graphs

  • Ramane, Harishchandra S.;Ashoka, K.;Patil, Daneshwari;Parvathalu, B.
    • Kyungpook Mathematical Journal
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    • v.61 no.1
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    • pp.155-168
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    • 2021
  • We express the Seidel Laplacian polynomial and Seidel signless Laplacian polynomial of a graph in terms of the Seidel polynomials of induced subgraphs. Further, we determine the Seidel Laplacian polynomial and Seidel signless Laplacian polynomial of the join of regular graphs.

THE RICCI CURVATURE ON DIRECTED GRAPHS

  • Yamada, Taiki
    • Journal of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.113-125
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    • 2019
  • In this paper, we consider the Ricci curvature of a directed graph, based on Lin-Lu-Yau's definition. We give some properties of the Ricci curvature, including conditions for a directed regular graph to be Ricci-flat. Moreover, we calculate the Ricci curvature of the cartesian product of directed graphs.

ON CYCLIC DECOMPOSITIONS OF THE COMPLETE GRAPH INTO THE 2-REGULAR GRAPHS

  • Liang, Zhihe
    • Journal of applied mathematics & informatics
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    • v.24 no.1_2
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    • pp.261-271
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    • 2007
  • The symbol C($m_1^{n_1}m_2^{n_2}{\cdots}m_s^{n_s}$) denotes a 2-regular graph consisting of $n_i$ cycles of length $m_i,\;i=1,\;2,\;{\cdots},\;s$. In this paper, we give some construction methods of cyclic($K_v$, G)-designs, and prove that there exists a cyclic($K_v$, G)-design when $G=C((4m_1)^{n_1}(4m_2)^{n_2}{\cdots}(4m_s)^{n_s}\;and\;v{\equiv}1(mod\;2|G|)$.

AN UPPER BOUND ON THE CHEEGER CONSTANT OF A DISTANCE-REGULAR GRAPH

  • Kim, Gil Chun;Lee, Yoonjin
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.507-519
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    • 2017
  • We present an upper bound on the Cheeger constant of a distance-regular graph. Recently, the authors found an upper bound on the Cheeger constant of distance-regular graph under a certain restriction in their previous work. Our new bound in the current paper is much better than the previous bound, and it is a general bound with no restriction. We point out that our bound is explicitly computable by using the valencies and the intersection matrix of a distance-regular graph. As a major tool, we use the discrete Green's function, which is defined as the inverse of ${\beta}$-Laplacian for some positive real number ${\beta}$. We present some examples of distance-regular graphs, where we compute our upper bound on their Cheeger constants.