含有k个悬挂点仙人掌图的原子键连通性指标

Atom-bond Connectivity Index of Cacti Graph with k Pendant Vertices

原子键连通性(ABC)指标为烷烃的稳定性和环烷烃的应变能力提供了一个好模型,其定义为ABC(G)=∑uv∈E(G)((d_u+d_v-2)/d_ud_v)^(1/2),其中d_u,d_v分别是图G中u,v点的度数.如果一个连通图G中的每个块要么是一条边要么是一个圈,则称图G为仙人掌图.该文的目标是获得了n个顶点含有k个悬挂点仙人掌图的ABC指标的最大值.

The atom-bond connectivity（ABC）index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes,which is defined as ABC（G）=∑uv∈E（G）√du＋dv-2/dudv,where d_u,d_vdenot the degree of vertex u,v of G.A cactus graph is a connected graph in which every block is an edge or a cycle.The aim of this paper is to obtain the maximum value of the ABC index among all n vertex cactus graphs with k pendant vertices.