摘要
The hyper-Wiener index is a kind of extension of the Wiener index,used for predicting physicochemical properties of organic compounds.The hyper-Wiener index W W(G)is defined as WW(G)=1/2∑u,v∈V(G)(dG(u,v)+d^2G(u,v))with the summation going over all pairs of vertices in G,dG(u,v)denotes the distance of the two vertices u and v in the graph G.In this paper,we study the minimum hyper-Wiener indices among all the unicyclic graph with n vertices and diameter d,and characterize the corresponding extremal graphs.
基金
Supported by the National Natural Science Foundation of China(Grant No.11871077)
the Natural Science Foundation of Anhui Province(Grant No.1808085MA04)
the Natural Science Foundation of Department of Education of Anhui Province(Grant No.KJ2017A362)。
