A proof of Alon's second eigenvalue conjecture and related problems

A d-regular graph has largest or first (adjacency matrix) eigenvalue 1 = d. Consider for an even d 4, a random d-regular graph model formed from d/2 uniform, independent permutations on {1, . . . , n}. We shall show that for any > 0 we have all eigenvalues aside from 1 = d are bounded by 2 d - 1 + with probability 1 - O(n- ), where =

• Type: Journal
• Year: 2004
• Where: CORR
• Authors: Joel Friedman
• Keywords: Adjacency Matrix, CORR 2004, D-regular Graph, Education, Random D-regular Graph