Explicit Computation of Cheeger Constants for some Classes of Graphs

Abstract

This article deals with the explicit computation of the Cheeger constant and its connection to understanding the properties of some classes of graphs. Cheeger constant is a measure of the connectivity or disconnectivity of graphs and gives the best possible way to cut a graph. More precisely, we deal with the problem of splitting the graph into two large components of approximately equal volumes by making a small cut, which is the idea of Cheeger constant of a graph. We computed the Cheeger constants for simple classes of graphs such as 2-comb graphs, cycle graphs, complete graphs, and cube graphs. We further analyzed the dynamics of Cheeger constants of the graphs under vertex-edge transformation.