Growth of graph powers
Combinatorics
2015-03-17 v1
Abstract
For a graph G, its rth power is constructed by placing an edge between two vertices if they are within distance r of each other. In this note we study the amount of edges added to a graph by taking its rth power. In particular we obtain that either the rth power is complete or "many" new edges are added. This is an extension of a result obtained by P. Hegarty for cubes of graphs.
Keywords
Cite
@article{arxiv.1005.2542,
title = {Growth of graph powers},
author = {Alexey Pokrovskiy},
journal= {arXiv preprint arXiv:1005.2542},
year = {2015}
}
Comments
6 pages, 1 figure