Number of walks and degree powers in a graph

M. A. Fiol; E. Garriga

doi:10.1016/j.disc.2008.03.025

paper

Number of walks and degree powers in a graph

arXiv:1206.0860 · doi:10.1016/j.disc.2008.03.025

Abstract

This note deals with the relationship between the total number of $k$ -walks in a graph, and the sum of the $k$ -th powers of its vertex degrees. In particular, it is shown that the the number of all $k$ -walks is upper bounded by the sum of the $k$ -th powers of the degrees.

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