Edge growth in graph powers
Combinatorics
2012-02-29 v1
Abstract
For a graph G, its rth power G^r has the same vertex set as G, and has an edge between any two vertices within distance r of each other in G. We give a lower bound for the number of edges in the rth power of G in terms of the order of G and the minimal degree of G. As a corollary we determine how small the ratio e(G^r)/e(G) can be for regular graphs of diameter at least r.
Keywords
Cite
@article{arxiv.1202.6085,
title = {Edge growth in graph powers},
author = {Alexey Pokrovskiy},
journal= {arXiv preprint arXiv:1202.6085},
year = {2012}
}