Metrically regular square of metrically regular bigraphs. I
Vladimír Vetchý (1991)
Archivum Mathematicum
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Vladimír Vetchý (1991)
Archivum Mathematicum
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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.
Lepovic, Mirko (2011)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: 05C50. We say that a regular graph G of order n and degree r і 1 (which is not the complete graph) is strongly regular if there exist non-negative integers t and q such that |SiЗSj| = t for any two adjacent vertices i and j, and |SiЗSj| = q for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex k. Let l1 = r, l2 and l3 be the distinct eigenvalues of a connected strongly regular graph. Let...
Fiol, M.A. (2000)
The Electronic Journal of Combinatorics [electronic only]
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Sizhong Zhou, Jiancheng Wu, Tao Zhang (2017)
Discussiones Mathematicae Graph Theory
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A spanning subgraph F of a graph G is called a P≥3-factor of G if every component of F is a path of order at least 3. A graph G is called a P≥3-factor covered graph if G has a P≥3-factor including e for any e ∈ E(G). In this paper, we obtain three sufficient conditions for graphs to be P≥3-factor covered graphs. Furthermore, it is shown that the results are sharp.
Polcyn, Joanna (2008)
The Electronic Journal of Combinatorics [electronic only]
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Ján Plesník (1974)
Czechoslovak Mathematical Journal
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Marián Sudolský (1978)
Mathematica Slovaca
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K. Shahul Hameed, K.A. Germina (2012)
Discussiones Mathematicae Graph Theory
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A graph whose edges are labeled either as positive or negative is called a signed graph. In this article, we extend the notion of composition of (unsigned) graphs (also called lexicographic product) to signed graphs. We employ Kronecker product of matrices to express the adjacency matrix of this product of two signed graphs and hence find its eigenvalues when the second graph under composition is net-regular. A signed graph is said to be net-regular if every vertex has constant net-degree,...