Graph-indexed random walks on special classes of graphs

TL;DR

This paper studies the average range of M-Lipschitz mappings on specific graph classes, providing formulas and asymptotic behavior for paths, complete graphs, bipartite graphs, and cycles.

Contribution

It offers explicit formulas and asymptotic analysis for the average range of M-Lipschitz mappings on well-known graph classes.

Findings

Closed formulas for average range on paths, complete graphs, bipartite graphs, and cycles.

Asymptotic behavior of the average range on these graph classes.

Insights into the structure of Lipschitz mappings on special graphs.

Abstract

We investigate the paramater of the average range of $M$-Lipschitz mapping of a given graph. We focus on well-known classes such as paths, complete graphs, complete bipartite graphs and cycles and show closed formulas for computing this parameter and also we conclude asymptotics of this parameter on these aforementioned classes.