Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 852406, 5 pages
Research Article

Bounds of Eigenvalues of K3,3-Minor Free Graphs

Faculty of Science, Huzhou Teachers College, Huzhou 313000, China

Received 17 February 2009; Accepted 11 May 2009

Academic Editor: Wing-Sum Cheung

Copyright © 2009 Kun-Fu Fang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The spectral radius ρ(G) of a graph G is the largest eigenvalue of its adjacency matrix. Let λ(G) be the smallest eigenvalue of G. In this paper, we have described the K3,3-minor free graphs and showed that (A) let G be a simple graph with order n7. If G has no K3,3-minor, then ρ(G)1+3n8. (B) Let G be a simple connected graph with order n3. If G has no K3,3-minor, then λ(G)2n4, where equality holds if and only if G is isomorphic to K2,n2.