On Irregularity In Graphs

Julie Haviland1
1Exeter College, Hele Road, Exeter EX4 4JS, U.K.

Abstract

Two parameters for measuring irregularity in graphs are the degree variance and the discrepancy. We establish best possible upper bounds for the discrepancy in terms of the order and average degree of the graph, and describe some extremal graphs, thereby providing analogues of results of [1], [4] and [5] for the degree variance.