Abstract
The Hosoya polynomial of a (molecular) graph G is defined as where d(G, k) is the number of vertex pairs at distance k in G. The calculation of the Hosoya polynomial of a (molecular) graph is a significant theme in Mathematical Chemistry, because from this polynomial much information about distance in the (molecular) graph, including several celebrated distance-based topological indices such as Wiener index, hyper-Wiener index, and Wiener vector, can be easily drawn. In this article, we give a general formula for computing the Hosoya polynomial of a capped armchair nanotube. We also apply this formula to derive the Hosoya polynomial of a small example of capped armchair nanotubes.
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