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COMBINATORICS
2006

The Diameter and Laplacian Eigenvalues of Directed Graphs

8 years 5 months ago
The Diameter and Laplacian Eigenvalues of Directed Graphs
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) 2 maxx log(1/(x)) log 2 2+ 1 where is the first non-trivial eigenvalue of the Laplacian and is the Perron vector of the transition probability matrix of a random walk on G.
Fan R. K. Chung
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Fan R. K. Chung
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