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The IRC Indices of Transformation and Derived Graphs

Author

Listed:
  • Haichang Luo

    (School of Intelligent Manufacturing, Zhanjiang University of Science and Technology, Zhanjiang 524300, China
    These authors contributed equally to this work.)

  • Sakander Hayat

    (School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
    These authors contributed equally to this work.)

  • 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)

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.

Suggested Citation

  • Haichang Luo & Sakander Hayat & Yubin Zhong & Zhongyuan Peng & Tamás Réti, 2022. "The IRC Indices of Transformation and Derived Graphs," Mathematics, MDPI, vol. 10(7), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1111-:d:783021
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