On Expanders Graphs: Parameters and Applications

Abstract

We give a new lower bound on the expansion coefficient of an edge-vertex graph of a $d$-regular graph. As a consequence, we obtain an improvement on the lower bound on relative minimum distance of the expander codes constructed by Sipser and Spielman. We also derive some improved results on the vertex expansion of graphs that help us in improving the parameters of the expander codes of Alon, Bruck, Naor, Naor, and Roth.