The number of labelled -arch graphs.
Lamathe, Cédric (2004)
Journal of Integer Sequences [electronic only]
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Lamathe, Cédric (2004)
Journal of Integer Sequences [electronic only]
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Unique minimum vertex dominating sets in the Cartesian product of a graph with a complete graph are considered. We first give properties of such sets when they exist. We then show that when the first factor of the product is a tree, consideration of the tree alone is sufficient to determine if the product has a unique minimum dominating set.
Qiao, Sheng Ning (2010)
Applied Mathematics E-Notes [electronic only]
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Discussiones Mathematicae - General Algebra and Applications
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Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n₊,n₋,n₀) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n₀ denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n - 2ν(G). Guo et al. [Ji-Ming Guo, Weigen Yan and Yeong-Nan Yeh. On the nullity and the matching number...