Bounds of Eigenvalues of K-3,K-3-Minor Free Graphs

The spectral radius. rho(G) of a graph G is the largest eigenvalue of its adjacency matrix. Let. lambda(G) be the smallest eigenvalue of G. In this paper, we have described the K-3,K-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. rho(G) <= 1 + root 3n-8. (B) Let G be a simple connected graph with order n >= 3. If G has no K-3,K-3-minor, then lambda(G) >= root 2n-4, where equality holds if and only if G is isomorphic to K-2,K-n-2. Copyright (C) 2009 Kun-Fu Fang.