Abstract
For a connected graph G, the RW index is defined as the sum of
the expected walks lengths between all pairs of vertices in the graph
G. This article is devoted to establish the explicit analytical
expressions for the expected value of the RW index of a random
polyphenylene chain. Furthermore, the average value and the sample
variance of the RW index with respect to the set of all polyphenylene
chains with n hexagons are obtained. The correlation between RW
index and Wiener index of the random polyphenylene chain is also
characterized. Finally, we prove the RW index of the random
polyphenylene chain is asymptotic to normal distributions.