Nonsingular (Vertex-Weighted) Block Graphs
Discrete Mathematics
2019-05-07 v1 Combinatorics
Abstract
A graph is \emph{nonsingular (singular)} if its adjacency matrix 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.
Cite
@article{arxiv.1905.01921,
title = {Nonsingular (Vertex-Weighted) Block Graphs},
author = {Ranveer Singh and Cheng Zheng and Naomi Shaked-Monderer and Abraham Berman},
journal= {arXiv preprint arXiv:1905.01921},
year = {2019}
}