On Graphs with Same Distance Distribution

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DOI: 10.4236/am.2017.86062    184 Downloads   283 Views  
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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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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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