On the irregularity of trees and unicyclic graphs with given matching number

Abstract

The irregularity of a graph G is defined as irr(G)= Σ _uv∈(G)|d_G(u)-d_G(v)|, where d _G(u) denotes the degree of vertex u and E(G) denotes the edge set of G. We determine the maximum irregularity of trees and unicyclic graphs with given number of vertices and matching number and characterize the extremal graphs.