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On Graphs with Same Distance Distribution
Chengyi University College, Jimei University, Xiamen, China
School of Mathematical Sciences, Xiamen University, Xiamen, China
- 1 Chengyi University College, Jimei University, Xiamen, China
- 2 School of Mathematical Sciences, Xiamen University, Xiamen, China
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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.
KeywordsDistance DistributionDistance MatrixWiener VectorHyper-Wiener Vector
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