Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651250 | Discrete Mathematics | 2007 | 5 Pages |
Abstract
Let G be a simple graph. Let λ1(G)λ1(G) and μ1(G)μ1(G) denote the largest eigenvalue of the adjacency matrix and the Laplacian matrix of G , respectively. Let ΔΔ denote the largest vertex degree. If G has just one cycle, thenλ1(G)⩽2Δ-1.The equality holds if and only if G≅CnG≅Cn.Andμ1(G)⩽Δ+2Δ-1.The equality holds if and only if G≅CnG≅Cn, n is even.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Shengbiao Hu,