Minimum total irregularity index of tricyclic graphs

الملخص EN

The quantitative characterization of the topological structures of irregular graphs has been demonstrated through several irregularity measures.

In the literature, not only different chemical and physical properties can be well comprehended but also quantitative structure-activity relationship (QSPR) and quantitative structure-property relationship (QSAR) are documented through these measures.

A simple graph G = (V, E) is a collection of V and E as vertex and edge sets respectively, with no multiple edges or loops.

Keeping in view the importance of various irregularity measures, in (Abdo et al., 2014a) the authors defined the total irregularity of a simple graph G = G(V, E) as irrt(G) = 1 2 P u,v∈V |dG(u) − dG(v)|, where dG(u) indicates the degree of the vertex u, where u ∈ V (G).

In this paper, we have determined the first minimum, second minimum and third minimum total irregularity index of the tricyclic graphs on the n vertices.