The Atom-Bond Connectivity and Geometric-Arithmetic Indices in Random Polyphenyl Chains

Abstract

The atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are two well-studied topological indices and found to be useful tools in QSPR and QSAR investigations. We have compared the excepted values of ABC and GA indices in random spiro chains. In this paper, we further establish simple explicit formulae for the expected values of ABC and GA indices in random polyphenyl chains which are graphs of a class of unbranched polycyclic aromatic hydrocarbons and present the average values of ABC and GA indices with respect to the set of all polyphenyl chains with n hexagons. Based on these formulae, we make comparisons between the expected values of ABC and GA indices in random polyphenyl chains.

Keywords:

• ABC index
• GA index
• random polyphenyl chain
• expected value

Acknowledgments

The authors would like to thank the anonymous referees for their constructive suggestions and valuable comments on this paper, which have contributed to the final preparation of the paper.

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

XK carried out the proofs of the main results in the manuscript. SW and JH participated in the design of the study and drafted the manuscript. All the authors read and approved the final manuscript.

Additional information

Funding

This project is supported by Science Foundation of Minjiang University under Grant No.MYK15004, Mjyp201608.