The diameter and Laplacian eigenvalues of directed graphs

被引：0
|
作者：
Chung, F [1 ]
机构：
[1] Univ Calif San Diego, La Jolla, CA 92093 USA
来源：
ELECTRONIC JOURNAL OF COMBINATORICS | 2006年 / 13卷 / 01期
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D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For undirected graphs it has been known for some time that one can bound the diameter using the eigenvalues. In this note we give a similar result for the diameter of strongly connected directed graphs G, namely D(G) <= [log(2-lambda)/(2)/2 min(x)log(1/phi(x))] + 1 where lambda is the first non-trivial eigenvalue of the Laplacian and phi is the Perron vector of the transition probability matrix of a random walk on G.
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页数：6
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