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Wiener indices in random cyclooctane chains. (English) Zbl 1438.05074

Summary: The Wiener index of a connected graph (molecule graph) \(G\) is the sum of the distances between all pairs of vertices of \(G\). In this paper, a simple exact formula is established for the expected value of the Wiener index in random cyclooctane chain. Moreover, we obtain the average value of the Wiener indices with respect to the set of all cyclooctane chains with \(n\) octagons.

MSC:

05C09 Graphical indices (Wiener index, Zagreb index, Randić index, etc.)
05C12 Distance in graphs
05C40 Connectivity
05C92 Chemical graph theory
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