Irregularity measures of graph

Abstract

Let G = (V,E), V = {1,2 …, n}, be a simple graph without isolated vertices, with vertex degree sequence d1 ≥ d2 ≥ … ≥ dn > 0, di = d(i). A graph G is regular if and only if d1 = d2 = … = dn. A graph invariant I(G) is measure of irregularity of graph G with the property I(G)=0 if and only if G is regular, and I(G)>0 otherwise. In this paper we introduce some new irregularity measures.