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摘要
The degree distance of a connected graph G, denoted by D'(G), is defined by
D'(G) = Sigma(x is an element of V(G)) d(x) Sigma(y is an element of V(G)) d(x, y),
where d(x) and d(x, y) are the degree of x and the distance between x and y, respectively. This parameter was proposed by Gutman and independently by Dobrynin and Kochetova as a weighted version of the Wiener index. In a previous paper [MATCH-Commun. Math. Comput. Chem. 2, 67(2012), 425-437] the authors determined nine graphs having smallest degree distances. Here a list of four trees of order n having smallest degree distances is deduced from this set of graphs provided n >= 10: one has diameter 2, two diameter 3 and one diameter 4. Since for trees the degree distance and the Wiener index are strongly related, it also follows that these trees have minimum Wiener index. Also four unicyclic connected graphs of order n having smallest degree distances are determined provided n >= 15 : one has diameter 2 and three diameter 3.
- 出版日期2015-7
