A note on the third invariant factor of the Laplacian matrix of a graph

Jian Wang; Yong-Liang Pan

A note on the third invariant factor of the Laplacian matrix of a graph

Combinatorics 2009-12-21 v1 Group Theory

Authors: Jian Wang , Yong-Liang Pan

Abstract

Let $G$ be a simple connected graph with $n\geq 5$ vertices. In this note, we will prove that $s_3(G)\leq n$ , and characterize the graphs which satisfy that $s_3(G)=n, n-1, n-2,$ or $n-3$ , where $s_3(G)$ is the third invariant factor of the Laplacian matrix of $G$ .

Keywords

Laplacian matrix invariant factor graph simple connected graph third invariant factor characterization

Cite

@article{arxiv.0912.3608,
  title  = {A note on the third invariant factor of the Laplacian matrix of a graph},
  author = {Jian Wang and Yong-Liang Pan},
  journal= {arXiv preprint arXiv:0912.3608},
  year   = {2009}
}

Comments

8 pages

Related papers

View all related →