English

Nonsingular Block Graphs: An Open Problem

Discrete Mathematics 2020-09-15 v3 Combinatorics

Abstract

A block graph is a graph in which every block is a complete graph. Let GG be a block graph and let A(G)A(G) be its (0,1)-adjacency matrix. Graph GG is called nonsingular (singular) if A(G)A(G) is nonsingular (singular). An interesting open problem, proposed in 2013 by Bapat and Roy, is to characterize nonsingular block graphs. In this article, we present some classes of nonsingular and singular block graphs and related conjectures.

Keywords

Cite

@article{arxiv.1803.03947,
  title  = {Nonsingular Block Graphs: An Open Problem},
  author = {Ranveer Singh and Cheng Zheng and Naomi Shaked-Monderer and Abraham Berman},
  journal= {arXiv preprint arXiv:1803.03947},
  year   = {2020}
}

Comments

In this draft the Conjectures are wrong

R2 v1 2026-06-23T00:48:52.105Z