Abstract
Let G be a graph with vertex set V(G). The total irregularity of G is defined as \(irr_t(G)=\sum _{\{u,v\}\subseteq V(G)}|deg_G(u)-deg_G(v)|\), where \(deg_G(v)\) 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.
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Acknowledgements
The authors indebted to professor Darko Dimitrov for reading the first draft of this paper and giving us his comments on the paper. We are also very grateful to the referees for their insightful comments and helpful suggestions. The research of authors was partially supported by the University of Kashan under grant no 364988/179.
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Ghalavand, A., Ashrafi, A.R. Ordering of c-cyclic graphs with respect to total irregularity. J. Appl. Math. Comput. 63, 707–715 (2020). https://doi.org/10.1007/s12190-020-01335-6
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DOI: https://doi.org/10.1007/s12190-020-01335-6