A Cheeger inequality of a distance regular graph using Green's function (vol 313, pg 2337, 2013)

Abstract

In the published version, we obtain a cheeger inequality of distance regular graphs in terms of the smallest positive eigenvalue of the Laplacian and a value alpha(d). However, we confirm that we need an additional condition for our Cheeger inequality of distance regular graphs: if tvr(i)((t)) > lambda(1)/1+lambda(1) for t <= alpha(d), then we obtain a Cheeger inequality of distance regular graphs as h(Gamma) < alpha(d)/lambda(1). (C) 2015 Elsevier B.V. All rights reserved.