AUTHOR=Raza Zahid , Akhter Shehnaz , Shang Yilun 

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

JOURNAL=Frontiers in Chemistry

VOLUME=Volume 10 - 2022

YEAR=2023

URL=https://www.frontiersin.org/journals/chemistry/articles/10.3389/fchem.2022.1067874

DOI=10.3389/fchem.2022.1067874

ISSN=2296-2646

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 an extended period, all these connection indices do not get attention.
Currently, Ali and Trinajsti\'c [Mol. Inform. 37, Art. No. 1800008, 2018] represented the Zagreb connection indices and found that these indices compared to basic Zagreb indices, give the finer value for the correlation coefficient for the $13$ physico-chemical characteristics of the octane isomers.
In this article, we acquire the formulae of expected values of the first Zagreb connection index of random cyclooctatetraene chain, random polyphenyls chain, and random chain network with $l$ number of octagons, hexagons, and pentagons, respectively.
Moreover, we study the extreme and average values of all the above random chains concerning the set of special chains:  the meta-chain, the ortho-chain, and the para-chain.