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

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

2009-12-18

arxiv.org/abs/0912.3608v1

Mathematics

Combinatorics

8 pages

Scientific paper

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 $G$.

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