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Wiener Indices in Two Types of Random Polygonal Chains

Hongyong Wang, Zhenghua Xu, Qin Jiang


The Wiener number of a connected graph is defined as the sum of distances between all pairs of vertices in G. In this paper, two explicit expressions are obtained for the expected values of the Wiener indices of two types of random polygonal chains, which are graphs of a class of linearly concatenated polygon-like structure, including polyphenyl hexagonal chain and pentagonal chain etc. To support our study, we provided some examples in the last section. Our formulaes can be used to compute the Winer numbers of unbranched concatenated polygon-like chains, and recover many results in the previous works.


Wiener number, random polygonal chain, expected value.

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