Cubic Cayley graphs with small diameter.
Curtin, Eugen (2001)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Curtin, Eugen (2001)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Alewyn P. Burger, Christina M. Mynhardt, William D. Weakley (2004)
Discussiones Mathematicae Graph Theory
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For a permutation π of the vertex set of a graph G, the graph π G is obtained from two disjoint copies G₁ and G₂ of G by joining each v in G₁ to π(v) in G₂. Hence if π = 1, then πG = K₂×G, the prism of G. Clearly, γ(G) ≤ γ(πG) ≤ 2 γ(G). We study graphs for which γ(K₂×G) = 2γ(G), those for which γ(πG) = 2γ(G) for at least one permutation π of V(G) and those for which γ(πG) = 2γ(G) for each permutation π of V(G).
Chao, Chong-Yun (1967)
Portugaliae mathematica
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Mariusz Woźniak (1999)
Discussiones Mathematicae Graph Theory
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An embedding of a simple graph G into its complement G̅ is a permutation σ on V(G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider some families of embeddable graphs such that the corresponding permutation is cyclic.
Z. Majcher (1981)
Colloquium Mathematicae
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Sooyeong Kim, Stephen J. Kirkland (2021)
Czechoslovak Mathematical Journal
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In spectral bisection, a Fielder vector is used for partitioning a graph into two connected subgraphs according to its sign pattern. We investigate graphs having Fiedler vectors with unbalanced sign patterns such that a partition can result in two connected subgraphs that are distinctly different in size. We present a characterization of graphs having a Fiedler vector with exactly one negative component, and discuss some classes of such graphs. We also establish an analogous result for...
Ponzoni, Ignacio, Sánchez, Mabel C., Brignole, Nélida B. (1998)
Electronic Journal of SADIO [electronic only]
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Bretto, A. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Igor' E. Zverovich, Olga I. Zverovich (2004)
Discussiones Mathematicae Graph Theory
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We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.
Zdzisław Skupień (2007)
Discussiones Mathematicae Graph Theory
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Ashwin Ganesan (2016)
Discussiones Mathematicae Graph Theory
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Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note, it is proved that two transposition graphs are isomorphic if and only if the corresponding two Cayley graphs are isomorphic. It is also proved that the transposition graph T(S) is edge-transitive if and only if the Cayley graph Cay(Sn,...
Grady D. Bullington, Linda L. Eroh, Steven J. Winters (2010)
Discussiones Mathematicae Graph Theory
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Explicit formulae for the γ-min and γ-max labeling values of complete bipartite graphs are given, along with γ-labelings which achieve these extremes. A recursive formula for the γ-min labeling value of any complete multipartite is also presented.
Brouwer, A.E., Spence, E. (2009)
The Electronic Journal of Combinatorics [electronic only]
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