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.
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