关于第二原子键连通指数（英文）

Note on the Second Atom-Bond Connectivity Index

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-2/nunv)1/2,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.

Given a simple graph G = （ V,E）, the second atom-bond connectivity index ABC2 of G is a new version of the atom-bond connectivity index as ABC2=ABC2（G）=∑uv∈E（G）（nu＋nv-2/nunv）1/2, where nu denotes the number of vertices of G whose distances to vertex u are smaller than those to other vertex v of the edge e = uv, and nv is defined analogously. In this paper, the trees with the first, second minimum and the first, second maximum ABC2 are characterized and the unicyclic graphs with minimum ABC2 are characterized.