汤自凯　侯耀平

摘 要 设G=（V，E）是简单连通图，第二原子键连通指数是一种的新的原子键连通指数ABC2，即

ABC2 = ABC2（G）=∑uv∈E（G）nu+nv-2nunv，

其中nu（nv）表示图中到边e=uv的顶点u（v）距离比到顶点v（u）距离小的顶点数.本文刻画了具有第一小、第二小与第一大、第二大第二原子键连通指数的树及具有最小第二原子键连通指数的单圈图.

关键词 第二原子键连通指数；树；单圈图

All graphs in this article are simple and finite. The vertex and edge sets of a graph G are V（G） and E（G）， respectively. The degree of a vertex u in G is denoted by degG（u） or du： The number of vertices of G is denoted by n（G） and is called the order of G. The distance dG（u，v） between vertices u and v∈V（G） is the number of edges on a shortest path connecting u and v in G. Molecular descriptors play a significant role in chemistry， pharmacology， etc， Among which， topological indices have a prominent place[1]. There are numerous topological descriptors that were applied in theoretical chemistry， especially in QSPR/QSAR research[2-5].

The atom-bond connectivity index is a novel topological index ABC and was conceived by Estrada， Torres， Rodriguez and Gutman[6]， defined as

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（编辑 胡文杰）