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 be a block graph and let be its (0,1)-adjacency matrix. Graph is called nonsingular (singular) if 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