%J Australasian Journal of Combinatorics
%L discovery10112671
%X For a graph G, its rth power G is defined as the graph with the same vertex set as G, and an edge between any two vertices whenever they are within distance r of each other in G. Motivated by a result from additive number theory, Hegarty raised the question of how many new edges G has when G is a regular, connected graph with diameter at least r. We address this question for r ≠ 3, 6. 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, for r ≠3, 6, we determine how small the ratio e(G )/e(G) can be for regular, connected graphs of diameter at least r. r r r
%O This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.
%T Edge growth in graph powers
%V 58
%A A Pokrovskiy
%N 2
%P 347-357
%D 2014