%0 Journal Article
%T A note on the third invariant factor of the Laplacian matrix of a graph
%A Jian Wang
%A Yong-Liang Pan
%J Mathematics
%D 2009
%I arXiv
%X 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 $G$.
%U http://arxiv.org/abs/0912.3608v1