TY  - JOUR
SP  - 347
VL  - 58
N1  - This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.
A1  - Pokrovskiy, A
JF  - Australasian Journal of Combinatorics
AV  - public
SN  - 2202-3518
Y1  - 2014/01/14/
TI  - Edge growth in graph powers
UR  - https://ajc.maths.uq.edu.au/pdf/58/ajc_v58_p347.pdf
EP  - 357
ID  - discovery10112671
N2  - 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
IS  - 2
ER  -