Nonsingular (Vertex-Weighted) Block Graphs

05/06/2019
by   Ranveer Singh, et al.
0

A graph G is nonsingular (singular) if its adjacency matrix A(G) is nonsingular (singular). In this article, we consider the nonsingularity of block graphs, i.e., graphs in which every block is a clique. Extending the problem, we characterize nonsingular vertex-weighted block graphs in terms of reduced vertex-weighted graphs resulting after successive deletion and contraction of pendant blocks. Special cases where nonsingularity of block graphs may be directly determined are discussed.

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