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 of a graph is the largest eigenvalue of its adjacency matrix. Let be the smallest eigenvalue of . In this paper, we have described the -minor free graphs and showed that (A) let be a simple graph with order . If has no -minor, then . (B) Let be a simple connected graph with order . If has no -minor, then , where equality holds if and only if is isomorphic to .