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doi:10.1016/0012-365X(93)90351-S 
Copyright © 1993 Published by Elsevier Science B.V. All rights reserved.
Irregularity strength of regular graphs of large degree
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Received 17 November 1988;
revised 5 March 1990.
Available online 27 March 2002.
Abstract
As defined by Chartrand et al. [2], the irregularity strength of a graph G is the smallest possible value of k for which we can assign positive integers not greater than k to the edges of G in such a way that the sums at each vertex are distinct.
We prove that, if G is an (n−3)- or (n−4)- regular graph of order n, the strength of G is 3 (except if G=K3,3); we conjecture that the irregularity strength of an r-regular graph of order n
2r is 3, except if G is Kl,l with l odd.
