Ordering of c-cyclic graphs with respect to total irregularity

Abstract

Let G be a graph with vertex set V(G). The total irregularity of G is defined as irrt(G)=∑{u,v}⊆V(G)|degG(u)−degG(v)|, where degG(v) is the degree of the vertex v of G. The cyclomatic number of G is defined as c=m−n+k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, an ordering of connected graphs and connected chemical graphs with cyclomatic number c with respect to total irregularity are given.