TITLE:
On Graphs with Same Distance Distribution
AUTHORS:
Xiuliang Qiu, Xiaofeng Guo
KEYWORDS:
Distance Distribution, Distance Matrix, Wiener Vector, Hyper-Wiener Vector
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.6,
June
19,
2017
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.