具有完美匹配和奇长直径的一类树的RCW数(英文)

Reciprocal Complementary Wiener Numbers of Trees with Perfect Matchings and Odd Diameter

连通图G的RCW数定义为RCW(G)=Σu,v V(G)1d+1 d(u,v|G),其中V(G)是图的点集,d(u,v|G)是点u与v之间的距离,d是图G的直径.首先定义了具有完美匹配和奇长直径的一类树,进而确定了这类树的最小,第二小,以及第三小RCW数.

The reciprocal complementary Wiener number of a connected graph G is defined as RCW（G） = ∑（u,v）v（G） 1/d＋1-d（u,v（G） where V（G） is the vertex set; d（u, vlG） is the distance between vertices u and v; d is the diameter of G. We firstly give a class of trees with perfect matchings and odd diameter, and we further determine the trees with the smallest, the second smallest and the third smallest reciprocal complementary Wiener numbers.