Bounds of Eigenvalues of K3, 3-Minor Free Graphs. (14th May 2009)

• Record Type: Journal Article
• Authors: Fang, Kun-Fu
• Other Names: Cheung Wing-Sum Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2009(2009)
• Publication Date: 2009-05-14
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2009/852406
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : The spectral radiusρ ( G ) of a graphG is the largest eigenvalue of its adjacency matrix. Letλ ( G ) be the smallest eigenvalue ofG . In this paper, we have described theK 3, 3 -minor free graphs and showed that (A) letG be a simple graph with ordern ≥ 7 . IfG has noK 3, 3 -minor, thenρ ( G ) ≤ 1 + 3 n − 8 . (B) LetG be a simple connected graph with ordern ≥ 3 . IfG has noK 3, 3 -minor, thenλ ( G ) ≥ − 2 n − 4, where equality holds if and only ifG is isomorphic toK 2, n − 2 .