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arXiv · 1905.01921

Nonsingular (Vertex-Weighted) Block Graphs

Ranveer Singh·Cheng Zheng·Naomi Shaked-Monderer·Abraham Berman
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Abstract

A graph $G$ is \emph{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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Ranveer Singh, Cheng Zheng, Naomi Shaked-Monderer, Abraham Berman. 2019-05-06. Nonsingular (Vertex-Weighted) Block Graphs. https://arxiv.org/abs/1905.01921

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