The expected values, variances and limiting distributions of Gutman index, Schultz index, multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index for a class of random chain networks

TL;DR

This paper derives the expected values, variances, and normal distribution limits of several graph indices for random chain networks, providing deeper mathematical understanding of their properties.

Contribution

It offers explicit formulas for the expectations and variances of multiple indices and establishes their asymptotic normality in random chain networks.

Findings

Explicit formulas for expected values of indices

Variance expressions for each index

Limiting distributions are normal

Abstract

There has been an upsurge of research on complex networks in recent years. The purpose of this paper is to study the mathematical properties of the random chain networks PGn with the help of graph theory. We first solve the expected value expressions of the Gutman index, Schultz index, multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index, and then we get the explicit expression formulas of their variances. Finally, we find that their limiting distributions all have the probabilistic and statistical significance of normal distribution.