Spanning trees and line graph eigenvalues

Details Spanning trees and line graph eigenvalues Spanning trees and line graph eigenvalues

2012-01-16

arxiv.org/abs/1201.3221v1

Mathematics

Combinatorics

Scientific paper

In this note, we prove if G is a graph with an odd number of vertices and an
odd number of spanning trees, then the adjacency matrix of the line graph of G
is nonsingular. We also show that if a connected graph G has 2^ts spanning
trees with s odd, then the nullity of the adjacency matrix of the line graph of
G is at most t+1.

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