TY - JOUR

T1 - Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network

AU - Raza, Zahid

AU - Akhter, Shehnaz

AU - Shang, Yilun

N1 - Funding information: This research was funded by the University of Sharjah.

PY - 2023/1/4

Y1 - 2023/1/4

N2 - 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.

AB - 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.

KW - average value

KW - expected value

KW - random cyclooctatetraene chain

KW - random polyphenyls chain

KW - zagreb connection indices

U2 - 10.3389/fchem.2022.1067874

DO - 10.3389/fchem.2022.1067874

M3 - Article

SN - 2296-2646

VL - 10

JO - Frontiers in Chemistry

JF - Frontiers in Chemistry

M1 - 1067874

ER -