The Expected Values of the First Zagreb and Randić Indices in Random Polyphenyl Chains

Abstract

The random polyphenyl chains with n hexagons are the special graphs of unbranched polycyclic aromatic hydrocarbons. The Randić (R) index and first Zagreb (M₁) index are two well-studied topological indices and found to be useful tools in QSPR and QSAR investigations. In this paper, we further establish simple explicit formulae for expected values of the Randić and first Zagreb indices in random polyphenyl chains and present the average values of these indices with respect to the set of all polyphenyl chains with n hexagons. Based on these formulae, we make comparisons between expected values of the Randić and first Zagreb indices in random polyphenyl chains.

Keywords:

• Average value
• first Zagreb index
• Randić index
• random polyphenyl chain

AMS SUBJECT CLASSIFICATION:

• 05C05
• 05C12

Disclosure statement

There are no conflicts of interest.