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For a connected graph G of order p and a non-empty subset S of the vertex set of G, the n-Steiner distance of S is defined to be the smallest size among all connected sub-graphs whose vertex sets contain. In this paper, we obtain the Hosoya polynomials of Steiner n-distance of some windmill graphs. Moreover, the Steiner Wiener indices of certain windmill graphs are also obtained. [ABSTRACT FROM AUTHOR]

It is very difficult to find a general formula for Hosoya polynomials of carbon nanotubes, so we have worked a program by using mathematica programming that finds Hosoya polynomials and many other mathematics parametrics of carbon nanotubes which consist of a single wall ((n, m) – nanotubes), for any positive integer n and m. Wiener index, average distance and diameter are mathematics parametrics that is related to chemical and physical properties and leading toward applied in a wide variety of applications. In this paper, we give general forms of adjacent matrices of types of carbon nanotubes which through finding Hosoya polynomial and Wiener index, and we managed to draw these types of nanotubes by two and three dimensions. [ABSTRACT FROM AUTHOR]