MINIMAL TOTAL IRREGULARITY INDEX OF THE TRICYCLIC GRAPHS

Authors

  • Hassan Ahmed National University of Computer and Emerging Sciences, Lahore

DOI:

https://doi.org/10.48129/kjs.13063

Abstract

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) can be well documented through these measures. A simple
graph G = (V,E) is a collection of V and E as a vertex and edge sets respectively, with no multiple
edges or loops. Keeping in view of the importance of various irregularity measures, in (Abdo and
Dimitrov 2012) the authors defined the total irregularity of a simple graph G = G(V,E) as
 irrt(G)=1/2 sum u,v\inV |dG(u) - dG(v)|
where dG(u) indicates the degree of the vertex u, where u \in V (G). In this paper, we determine the
first minimal, second minimal and third minimal total irregularity index of the tricyclic graphs on the n
vertices.

Published

08-01-2022

Issue

Section

Mathematics