On the Laplacian spread of graphs

✍ Scribed by Mingqing Zhai; Jinlong Shu; Yuan Hong

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 238 KB
• Volume: 24
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2011.06.005

✦ Synopsis

The Laplacian spread s(G) of a graph G is defined to be the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of G. Several upper bounds of Laplacian spread and corresponding extremal graphs are obtained in this paper.

Particularly, if G is a connected graph with n(≥ 5) vertices and m(n -1 ≤ m ≤ n + 1) edges, then s(G) ≤ n -1 with equality if and only if G is obtained from K 1,n-1 by adding mn + 1 edges.