The statistical analysis for Sombor indices in a random polygonal chain networks

TL;DR

This paper derives the statistical distributions, expected values, and variances of Sombor indices in various random polygonal chain networks, showing they tend to normal distribution as the chain length increases.

Contribution

It provides the first analytical expressions for the distributions, expected values, and variances of Sombor indices in random polygonal chains, linking network structure to statistical properties.

Findings

Expected values and variances are obtained for specific chain types.

Sombor indices follow a normal distribution for large chain sizes.

The end connection distribution influences the overall index distribution.

Abstract

The Sombor indices, a new category of degree-based topological molecular descriptors, have been widely investigated due to their excellent chemical applicability. This paper aims to establish Sombor indices distributions in random polygonal chain networks and to achieve expressions of the expected 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 random chain network follows a binomial distribution, the Sombor indices of any chain network follow the normal distribution when the number of polygons connected by the chain, indicated by n, approaches infinity. Keywords: Degree distribution; Polygonal chains; Expected value; Variance; Sombor indices.