Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network

Zahid Raza; Shehnaz Akhter; Yilun Shang

doi:10.3389/fchem.2022.1067874

Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network

Front Chem. 2023 Jan 4:10:1067874. doi: 10.3389/fchem.2022.1067874. eCollection 2022.

Authors

Zahid Raza¹, Shehnaz Akhter², Yilun Shang³

Affiliations

¹ Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates.
² School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan.
³ Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne, United Kingdom.

Abstract

The Zagreb connection indices are the known topological descriptors of the graphs that are constructed from the connection cardinality (degree of given nodes lying at a distance 2) presented in 1972 to determine the total electron energy of the alternate hydrocarbons. For a long time, these connection indices did not receive much research attention. Ali and Trinajstić [Mol. Inform. 37, Art. No. 1800008, 2018] examined the Zagreb connection indices and found that they compared to basic Zagreb indices and that they provide a finer value for the correlation coefficient for the 13 physico-chemical characteristics of the octane isomers. This article acquires the formulae of expected values of the first Zagreb connection index of a random cyclooctatetraene chain, a random polyphenyls chain, and a random chain network with l number of octagons, hexagons, and pentagons, respectively. The article presents extreme and average values of all the above random chains concerning a set of special chains, including the meta-chain, the ortho-chain, and the para-chain.

Keywords: average value; expected value; random cyclooctatetraene chain; random polyphenyls chain; zagreb connection indices.