Raza Zahid, Akhter Shehnaz, Shang Yilun
Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates.
School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan.
Front Chem. 2023 Jan 4;10:1067874. doi: 10.3389/fchem.2022.1067874. eCollection 2022.
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 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.
萨格勒布连接指数是由1972年提出的连接基数（距离为2的给定节点的度数）构建的图的已知拓扑描述符，用于确定交替烃的总电子能量。长期以来，这些连接指数没有受到太多的研究关注。阿里和特里纳伊斯特奇[《分子信息学》37，第1800008号，2018年]研究了萨格勒布连接指数，发现它们与基本萨格勒布指数相比，为辛烷异构体的13种物理化学特性的相关系数提供了更精确的值。本文分别获得了具有八边形、六边形和五边形数量的随机环辛四烯链、随机聚苯链和随机链网络的第一萨格勒布连接指数的期望值公式。本文给出了上述所有随机链相对于一组特殊链（包括间位链、邻位链和对位链）的极值和平均值。
