Linear time algorithm to check the singularity of block graphs

08/10/2018

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by   Ranveer Singh, et al.

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A block graph is a graph in which every block is a complete graph. 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 is an interesting open problem proposed by Bapat and Roy in 2013. In this article, we give a linear time algorithm to check whether a given block graph is singular or not.