Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9513623 | Discrete Mathematics | 2005 | 9 Pages |
Abstract
In this paper we study the number of spanning forests of a graph. Let G be a connected simple graph. (1) We give a lower bound for the number of spanning forests of G in terms of the edge connectivity of G. (2) We give an upper bound for the number of rooted spanning forests of G. (3) We describe the elementary symmetric functions of inverse positive Laplacian eigenvalues of a tree. (4) We determine all Laplacian integral graphs with prime number of spanning trees. (5) We give a simple proof of a theorem of K. Hashimoto on Ihara zeta function.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yasuo Teranishi,