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.
Cite this paper
Qiu, X. and Guo, X. (2017) On Graphs with Same Distance Distribution. Applied Mathematics, 8, 799-807. doi: 10.4236/am.2017.86062.
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