On Irregularity of Graphs

Abstract

The graph’s irregularity is the sum of the absolute values of the differences of degrees of pairs of adjacent vertices in the graph. We provide various upper bounds for the irregularity of a graph, especially for $K_{r+1}$-free graphs, where $K_{r+1}$ is a complete graph on $r+1$ vertices, and trees and unicyclic graphs of given number of pendant vertices.