On the isoperimetric spectrum of graphs and its approximations

@article{Daneshgar2010OnTI,
title={On the isoperimetric spectrum of graphs and its approximations},
author={Amir Daneshgar and Hossein Hajiabolhassan and Ramin Javadi},
journal={J. Comb. Theory, Ser. B},
year={2010},
volume={100},
pages={390-412}
}

In this paper we consider higher isoperimetric numbers of a (finite directed) graph. In this regard we focus on the nth mean isoperimetric constant of a directed graph as the minimum of the mean outgoing normalized flows from a given set of n disjoint subsets of the vertex set of the graph. We show that the second mean isoperimetric constant in this general setting, coincides with (the mean version of) the classical Cheeger constant of the graph, while for the rest of the spectrum we show that… CONTINUE READING