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arXiv · 1206.0860

Number of walks and degree powers in a graph

M. A. Fiol·E. Garriga
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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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M. A. Fiol, E. Garriga. 2012-06-05. Number of walks and degree powers in a graph. https://doi.org/10.1016/j.disc.2008.03.025

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