Nonsingular Block Graphs: An Open Problem
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A block graph is a graph in which every block is a complete graph (clique). Let G be a block graph and let A(G) be its (0,1)-adjacency matrix. Graph G is called nonsingular (singular) if A(G) is nonsingular (singular). Characterizing nonsingular block graphs, other than trees, is an interesting open problem. In this article, we give some classes of nonsingular and singular block graphs and related conjectures.
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