On Γ-regular graphs
J. Płonka (1982)
Colloquium Mathematicae
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J. Płonka (1982)
Colloquium Mathematicae
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Vladimír Vetchý (1992)
Archivum Mathematicum
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Metrically regular bigraphs the square of which are metrically regular graphs are investigated in the case of graphs with 6 distinct eigenvalues (these eigenvalues can have variuos multiplicities).
G. Sierksma (1987)
Applicationes Mathematicae
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Fiol, M.A. (2000)
The Electronic Journal of Combinatorics [electronic only]
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Volkmann, Lutz (2007)
The Electronic Journal of Combinatorics [electronic only]
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Ravindra B. Bapat, Masoud Karimi (2017)
Discussiones Mathematicae Graph Theory
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Graphs G and H are called cospectral if they have the same characteristic polynomial. If eigenvalues are integral, then corresponding graphs are called integral graph. In this article we introduce a construction to produce pairs of cospectral integral regular graphs. Generalizing the construction of G4(a, b) and G5(a, b) due to Wang and Sun, we define graphs 𝒢4(G,H) and 𝒢5(G,H) and show that they are cospectral integral regular when G is an integral q-regular graph of order m and H...
Zoran S. Radosavljević (1981)
Publications de l'Institut Mathématique
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Bostjan Brešar (2003)
Discussiones Mathematicae Graph Theory
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We consider classes of graphs that enjoy the following properties: they are closed for gated subgraphs, gated amalgamation and Cartesian products, and for any gated subgraph the inverse of the gate function maps vertices to gated subsets. We prove that any graph of such a class contains a peripheral subgraph which is a Cartesian product of two graphs: a gated subgraph of the graph and a prime graph minus a vertex. Therefore, these graphs admit a peripheral elimination procedure which...
Mohar, Bojan (1984)
Publications de l'Institut Mathématique. Nouvelle Série
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Vladimír Vetchý (1993)
Archivum Mathematicum
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The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only one table of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter (7 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter see [7] and [8].
Lorenzo Traldi (2016)
Discussiones Mathematicae Graph Theory
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We show that every 3-regular circle graph has at least two pairs of twin vertices; consequently no such graph is prime with respect to the split decomposition. We also deduce that up to isomorphism, K4 and K3,3 are the only 3-connected, 3-regular circle graphs.