The Variance, Skewness and Limiting Behavior of the Wiener Index for Random Pentagonal Chain

Abstract

 The network graph is a tool to study various complex systems in real world situations such as social networks, food webs, internet etc. In this work, we study the statistical parameters of the random pentagonal chain network, PG_n like dispersion and asymmetry. We establish the explicit formulas for the expected value, variance and skewness of the Wiener index. Further, we obtain that the index obeys normal distribution asymptotically.