The statistical analysis for Sombor indices in a randompolygonal chain networks

The Sombor indices, a new category of degree-based topological molecular descriptors, havebeen widely investigated due to their excellent chemical applicability. This paper aims to establishSombor indices distributions in random polygonal chain networks and to achieve expressions of theexpected values and variances. The expected values and variances of the Sombor indices for polyonino,pentachain, polyphenyl, and cyclooctane chains are obtained. Since the end connection of a randomchain network follows a binomial distribution, the Sombor indices of any chain network follow the normaldistribution when the number of polygons connected by the chain, indicated by n, approaches infinity.