On the adjacency matrix of a block graph

Abstract

A block graph is a graph in which every block is a complete graph. Let G be a block graph and let A be the adjacency matrix of G. We first obtain a formula for the determinant of A over reals. It is shown that A is nonsingular over IF2 if and only if the removal of any vertex from G produces a graph with exactly one odd component. A formula for the inverse… (More)

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