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**publisher and metadata sources**).In this article, two necessary conditions for a graph to have an equality of the second largest Laplacian eigenvalue λ 2 ( G ) and its lower bound d 2 ( G ) are presented. Some of the graphs who… Continue Reading

The sandpile group of a graph is a refinement of the number of spanning trees of the graph and is closely connected to the graph Laplacian. In this note the sandpile group of P"4xC"n is proved to be… Continue Reading

Abstract Let G σ be a weighted oriented graph, which is obtained from a simple weighted undirected graph by assigning an orientation to each of its edges. For a (weighted) oriented graph G σ , the… Continue Reading

Abstract A strongly connected directed graph in which any two directed cycles of it share at most one common vertex is called a cactoid digraph. Let D be its distance matrix. By a theorem of Graham,… Continue Reading

A b s t r a c t. Let G be a graph with n vertices and m edges. Then its cyclomatic number is c = m n + 1. If 1; 2;:::; n are the eigenvalues of G, then its energy is E(G) = ∑ n=1 j ij. The graph G is… Continue Reading