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math.CO2000★ 17 cited
On the chromatic roots of generalized theta graphs
Jason Brown, Carl Hickman, Alan D. Sokal +1
The generalized theta graph Θ_{s_1,...,s_k} consists of a pair of endvertices joined by k internally disjoint paths of lengths s_1,...,s_k \ge 1. We prove that the roots of the chr…
math.CO2000★ 25 cited
The critical group of a directed graph
David G. Wagner
The critical group K(G) of a directed graph G=(V,E) is the cokernel of the transpose of the Laplacian matrix of G acting on the integer lattice Z^V. For undirected graphs G, this h…