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On Graphs with Same Distance Distribution

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Document pages: 10 pages

Abstract: In the present paper we investigate the relationship between Wiener number W, hyper-Wiener number R, Wiener vectors WV, hyper-Wiener vectors HWV, Wiener polynomial H, hyper-Wiener polynomial HH and distance distribution DD of a (molecular) graph. It is shown that for connected graphs G and G*, the following five statements are equivalent:  ; and if G and G* have same distance distribution DD then they have same W and R but the contrary is not true. Therefore, we further investigate the graphs with same distance distribution. Some construction methods for finding graphs with same distance distribution are given.

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