The total irregularity of a graph

Abstract

In this note a new measure of irregularity of a graph G is introduced. It is named the total irregularity of a graph and is defined as irrt(G) = 1/2 ∑u,vεV (G)|dG(u) - dG(v)| , where dG(u) denotes the degree of a vertex u ∑ V (G). All graphs with maximal total irregularity are determined. It is also shown that among all trees of the same order the star has the maximal total irregularity. © 2014 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.