Ordering of c-cyclic graphs with respect to total irregularity

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)|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$irr_t(G)=\sum _{\{u,v\}\subseteq V(G)}|deg_G(u)-deg_G(v)|$$\end{document}, where degG(v)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$deg_G(v)$$\end{document} is the degree of the vertex v of G. The cyclomatic number of G is defined as c=m-n+k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c = m - n + k$$\end{document}, 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.