The IRC Indices of Transformation and Derived Graphs

Haichang Luo, Sakander Hayat, Yubin Zhong, Zhongyuan Peng and Tamás Réti
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Haichang Luo: School of Intelligent Manufacturing, Zhanjiang University of Science and Technology, Zhanjiang 524300, China
Sakander Hayat: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
Yubin Zhong: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
Zhongyuan Peng: Department of Social Sciences, Maoming Polytechnic, Maoming 525000, China
Tamás Réti: Donát Bánki Faculty of Mechanical and Safety Engineering, Obuda University, Népszínház str. 8, H-1081 Budapest, Hungary

Mathematics, 2022, vol. 10, issue 7, 1-18

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 R C closely correlates with the normal boiling point T b p and the standard heat of formation Δ H f o of lower benzenoid hydrocarbons. The correlation models that fit the data efficiently for both T b p and Δ H f o are linear. We develop further mathematical properties of I R C 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 R C index of graphs.

Keywords: irregularity index; physicochemical property; QSAR model; benzenoid hydrocarbon; transformation graph; derived graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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