Bounds of Eigenvalues of K3,3-Minor Free Graphs

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 LetG be a simple connected graph with order n ≥ 3. IfG has noK3,3-minor, then λ G ≥ −√2n − 4, where equality holds if and only if G is isomorphic to K2,n−2.