Statistical Analyses of a Class of Random Pentagonal Chain Networks with respect to Several Topological Properties

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 pentagonal chain networks $\text{PE}{\text{C}}_n$ with the help of graph theory. Based on the networks $\text{PE}{\text{C}}_n$ , we first obtain 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.