Bounds of Eigenvalues of -Minor Free Graphs

Kun-Fu Fang
2009 Journal of Inequalities and Applications  
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 K 3,3 -minor free graphs and showed that A let G be a simple graph with order n ≥ 7. If G has no K 3,3 -minor, then ρ G ≤ 1 √ 3n − 8. B Let G be a simple connected graph with order n ≥ 3. If G has no K 3,3 -minor, then λ G ≥ − √ 2n − 4, where equality holds if and only if G is isomorphic to K 2,n−2 .
doi:10.1155/2009/852406 fatcat:ebikld2ldrantbzu5hahp63oea