积图的Steiner k-hyper Wiener指标  

Steiner k-hyper Wiener index of graph products

作　　者：王朝平 刘蒙蒙 WANG Chaoping;LIU Mengmeng(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《运筹学学报(中英文)》2025年第1期216-224,共9页Operations Research Transactions

基　　金：甘肃高等学校创新能力提升项目(No.2019A-37)。

摘　　要：令图G是一个连通图。当2≤k≤n-1时,图G的Steiner k-hyper Wiener指标定义为SWW_(k)(G)=1/2∑_(S■V(G),|S|=k)dG(S)+1/2∑_(S■V(G),|S|=k)dG(S)^(2),其中dG(S)表示图G中S的Steiner距离,即连通图G中包含点集S的最小连通子图的边数。本文中我们确定了连图和字典积图的Steiner k-hyper Wiener指标的表达式,给出了笛卡尔积图,聚类图和冠状图的Steinerk-hyper Wiener指标的下限。Let G be a connected graph.For 2≤k≤n-1,the Steiner khyper Wiener index SWW_(k)G)is defined as SWW_(k)(G)=1/2∑_(S■V(G),|S|=k)dG(S)+1/2∑_(S■V(G),|S|=k)dG(S)^(2)where d_G(S)is the Steiner distance of S,means the minimum size of a connected subgraph which vertex set contains S.In this paper,we establish expressions for the Steiner k-hyper Wiener index on the join and lexicographical product of graphs and give lower bounds for the Steiner k-hyper Wiener index on cartesian,cluster and corona product of graphs.

关 键 词：积图 Steiner k-hyper Wiener指标 Steiner距离 

分 类 号：O157.5[理学—数学]