Irregularity measures of graph

Abstract

Let G = (V, E), V = {1, 2, . . . , n}, be a simple graph without isolated vertices, with vertex degree sequenceis 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.

Two Irregularity Measures Possessing High Discriminatory Ability

“…In Table 1, those existing irregularity measures (together with their definitions and some relevant references) are given which will be discussed in this paper. Further detail about the existing irregularity measures can be found in the surveys [6,24], papers [10,11,18,32,33,38,40] and in the references listed therein. It is well-known fact that there does not exist any n-vertex graph whose all degrees are different for n > 1.…”