Graphs with maximal [formula omitted] irregularity

Abstract

A natural extension of the well-known Albertson irregularity index is the recently introduced σ irregularity index. For a simple graph G with an edge set E(G), the σ irregularity index is defined as σ(G)=∑uv∈E(G)(dG(u)−dG(v))2, where dG(v) denotes the degree of the vertex v of G. Here, we characterize general graphs with maximal σ irregularity. We also present lower bounds on the maximal σ irregularity of graphs with fixed minimal and/or maximal vertex degrees.