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.

Abstract

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 n≥7. If G has no K3,3-minor, then ρ(G)≤1+3n−8. (B) Let G be a simple connected graph with order n≥3. If G has no K3,3-minor, then λ(G)≥−2n−4, where equality holds if and only if G is isomorphic to K2,n−2.