Title
Hosoya Polynomials of Steiner Distance of Some Graphs: Hosoya Polynomials & Wiener Indices of Graphs,Used
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The Steiner ndistance, d(S), of a nonempty n subset S of vertices of a graph G is defined to be the size of the smallest connected subgraph T(S) containing S. The Hosoya polynomial of Steiner n distance of a connected graph G is denoted by Hn* (G;x). In this work, we obtain Hosoya polynomials of Steiner ndistance(n is greater than or equal to 3 and less than or equal to the order of the graph) of some particular graphs; for other prescribed graphs, we obtain Hosoya polynomials of Steiner 3 distance. For some graphs G, we find reduction formulas for Hn*(G;x) or H3*(G;x). Wiener indices of the Steiner ndistance of most of the particular graphs and composite graphs considered here are also obtained. Moreover, the diameter of the Steiner ndistance for each one of these graphs is determined. Furthermore, Wiener index theorem for trees, which is due to H. Wiener, is generalized to Steiner n distance of trees.
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