The Harmonic and Second Zagreb Indices in Random Polyphenyl and Spiro Chains

Abstract

The polyphenyl chains with n hexagons are the special graphs of unbranched polycyclic aromatic hydrocarbons. The main objective of this study is to find the expected values of the harmonic and second Zagreb indices of this class of hydrocarbons. The average values of the harmonic and second Zagreb indices with respect to the set of all random polyphenyl and spiro chains have been determined. Finally, the comparisons between the expected values of these indices with respect to the random polyphenyl and spiro chains, have been outlined.

Keywords:

• Harmonic index
• second Zagreb index
• random polyphenyl chain
• random spiro chain
• expected value

Subjclass[2010] Primary:

• 05C09
• 05C92
• 05C90

Additional information

Funding

This research work is funded by the University of Sharjah under the Project #1802144068 and MASEP Research Group.