A New Upper Bound for Laplacian Graph Eigenvalues

Journal Article · Thu Nov 06 00:00:00 EST 2008 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3037077· OSTI ID:21251776

Shengbiao, Hu ^[1]

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1. Department of Mathematics, Qinghai Nationalities College, Xinig, Qinghai 810007 (China)

Let G = (V,E) be a graph with vertex set V = {l_brace}v{sub i},V{sub 2},...,v{sub n}{r_brace}. The degree of v{sub i} and the average degree of the adjacent vertices of v{sub i} are denoted by d{sub i} and m{sub v{sub i}}, respectively. In this paper, we prove that max {l_brace}(d{sub v}m{sub v}/d{sub u})+(d{sub u}m{sub u}/d{sub v}):uv(set-membership sign)E{r_brace} is an upper bound for the largest Laplacian eigenvalue of G, the equality holds if G is a d-regular bipartite graph.

• OSTI ID: 21251776
• Journal Information: AIP Conference Proceedings, Vol. 1060, Issue 1; Other Information: DOI: 10.1063/1.3037077; (c) 2008 American Institute of Physics; IeCCS 2007: International electronic conference on computer science, 28 June - 8 July 2007; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENFUNCTIONS
EIGENVALUES
GRAPH THEORY
LAPLACIAN
NUMERICAL ANALYSIS