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THe largest eigenvalue of sparse random graphs by Krivelevich, Michael; Sudakov, Benny is a scholarly article available to read on EtoBox.

What is THe largest eigenvalue of sparse random graphs about?

We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n,p) satisfies almost surely: \lambda_1(G)=(1+o(1))max{\sqrt{\Delta},np}, where \Delta is a maximal degree of G, and the o(1) term tends to zero as max{\sqrt{\Delta},np} tends to infinity.

Author

Krivelevich, Michael; Sudakov, Benny

Published

2001

Language

EN