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We introduce and study an eigenvalue upper bound p(G) on the maximum cut mc (G) of a weighted graph. The function ~o(G) has several interesting properties that resemble the behaviour of mc (G). The following results are presented. We show that q~ is subadditive with respect to amalgam, and additive with respect to disjoint sum and 1-sum. We prove that ~(G)(More)
Relations between Laplacian eigenvectors and eigenvalues and the existence of almost equitable partitions (which are generalizations of equitable partitions) are presented. Furthermore, on the basis of some properties of the adjacency eigenvectors of a graph, a necessary and sufficient condition for the graph to be primitive strongly regular is introduced.