1 research outputs found
Nonsingular (Vertex-Weighted) Block Graphs
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