Abstract
An irregularity index IR(Γ) of a graph Γ is a nonnegative numeric quantity (i.e., IR(Γ)≥0) such that IR(Γ)=0 iff Γ is a regular graph. In this paper, we show that IRC closely correlates with the normal boiling point Tbp and the standard heat of formation ΔHfo of lower benzenoid hydrocarbons. The correlation models that fit the data efficiently for both Tbp and ΔHfo are linear. We develop further mathematical properties of IRC 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 IRC index of graphs.
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