The IRC Indices of Transformation and Derived Graphs

Abstract

An irregularity index I R(Γ) of a graph Γ is a nonnegative numeric quantity (i.e., I R(Γ) ≥ 0) such that I R(Γ) = 0 iff Γ is a regular graph. In this paper, we show that I RC closely correlates with the normal boiling point Tbp and the standard heat of formation ∆Hof of lower benzenoid hydrocarbons. The correlation models that fit the data efficiently for both Tbp and ∆Hof are linear. We develop further mathematical properties of I RC by calculating its exact expressions for the recently introduced transformation graphs as well as certain derived graphs, such as the total graph, semi-total point graph, subdivision graph, semi-total line graph, double, strong double, and extended double cover graphs. Some open problems are proposed for further research on the I RC index of graphs.