Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4657268 | Journal of Combinatorial Theory, Series B | 2008 | 30 Pages |
Abstract
Let M denote the Laplacian matrix of a graph G. Associated with G is a finite group Φ(G), obtained from the Smith normal form of M, and whose order is the number of spanning trees of G. We provide some general results on the relationship between the eigenvalues of M and the structure of Φ(G), and address the question of how often the group Φ(G) is cyclic.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics