Graphs with maximal [Formula presented] irregularity

Abstract

© 2018 Elsevier B.V. A natural extension of the well-known Albertson irregularity index is the recently introduced [Formula presented] irregularity index. For a simple graph [Formula presented] with an edge set [Formula presented], the [Formula presented] irregularity index is defined as [Formula presented], where [Formula presented] denotes the degree of the vertex [Formula presented] of [Formula presented]. Here, we characterize general graphs with maximal [Formula presented] irregularity. We also present lower bounds on the maximal [Formula presented] irregularity of graphs with fixed minimal and/or maximal vertex degrees.