On k-regular graphs containing (k-1)-regular subgraphs
G. Sierksma (1987)
Applicationes Mathematicae
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G. Sierksma (1987)
Applicationes Mathematicae
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Zoran S. Radosavljević (1981)
Publications de l'Institut Mathématique
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G.L. Chia, C.S. Gan (2004)
Discussiones Mathematicae Graph Theory
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This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.
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).
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...
Gera, Ralucca, Shen, Jian (2008)
The Electronic Journal of Combinatorics [electronic only]
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Fiol, M.A. (2000)
The Electronic Journal of Combinatorics [electronic only]
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Andrey A. Dobrynin, Leonid S. Mel'nikov, Artem V. Pyatkin (2007)
Discussiones Mathematicae Graph Theory
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In 1960, Dirac put forward the conjecture that r-connected 4-critical graphs exist for every r ≥ 3. In 1989, Erdös conjectured that for every r ≥ 3 there exist r-regular 4-critical graphs. A method for finding r-regular 4-critical graphs and the numbers of such graphs for r ≤ 10 have been reported in [6,7]. Results of a computer search for graphs of degree r = 12,14,16 are presented. All the graphs found are both r-regular and r-connected.
Hailong Hou, Yanhua Song, Rui Gu (2017)
Open Mathematics
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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.
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].
Mohsen Ghasemi (2012)
Colloquium Mathematicae
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A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper, tetravalent one-regular graphs of order 3p², where p is a prime, are classified.
D. M. Cardoso, D. Cvetković (2006)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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