几类图的原子键和连通性(ABS)指标

Atom-Bond Sum-Connectivity (ABS) Index of Some Graphs

摘要: 原子键连通性(ABC)指标与和连通性(SC)指标属于连通性指标的变体类，Ali等人将SC指标和ABC指标的核心思想结合起来提出了一种新的分子拓扑指标，称原子键和连通性(ABS)指标。图$G$ 的原子键和连通性指标表示为$ABS\left(G\right)={\displaystyle \sum _{uv\in E\left(G\right)}{\left(1-2{\left(d_u+d_v\right)}^{-1}\right)}^{1/2}}$ ，其中$d_u$ 为图$G$ 中顶点$u$ 的度数。本文主要讨论格子图、锯齿型纳米管$TUH{C}_6\left[2p,q\right]$ 、扶手椅型纳米管$TUV{C}_6\left[2p,q\right]$ 、硅酸盐链$C{S}_n$ 、$n$ 长的$K_n$ 链、直链$L_n$ 、锯齿链$Z_n$ 、双直链$L_{2\times n}$ 、双锯齿链$Z_{2\times n}$ 等化学图以及几类仙人掌链和一些特殊图的ABS指标。

Abstract: Atom-bond connectivity (ABC) index and sum-connectivity (SC) index belong to the variant class of connectivity index, Ali et al. introduced a new molecular topological index called atom-bond sum-connectivity (ABS) index by combining the core ideas of SC index and ABC index. The Atom-bond sum-connectivity index of a graph G is$ABS\left(G\right)={\displaystyle \sum _{uv\in E\left(G\right)}{\left(1-2{\left(d_u+d_v\right)}^{-1}\right)}^{1/2}}$ , where $d_u$ is the degree of the vertex $u$ in the graph G. In this paper, we mainly discuss the ABS indices of the following chemical graphs: grid graphs, zigzag polyhex nanotube $TUH{C}_6\left[2p,q\right]$ , armchair polyhex nanotube $TUV{C}_6\left[2p,q\right]$ , silicate chain $C{S}_n$ , chain $K_n$ , straight chain $L_n$ , zigzag chain $Z_n$ , double straight chain $L_{2\times n}$ , double zigzag chain $Z_{2\times n}$ , several types of cactus chains and ABS index of some special graphs.