On Cayley Graphs on the Symmetric Group Generated by Tranpositions

Given a connected graph, X, we denote by 2 = 2(X) its smallest non-zero Laplacian eigenvalue. In this paper we show that among all sets of n - 1 transpositions which generate the symmetric group, Sn, the set whose associated Cayley graph has the highest 2 is the set {(1, n), (2, n), . . . , (n - 1, n)} (or the same with n and i

• Type: Journal
• Year: 2000
• Where: COMBINATORICA
• Authors: Joel Friedman
• Keywords: Cayley Graph, COMBINATORICA 2000, Connected Graph, Non-zero Laplacian Eigenvalue