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运筹学学报 >

2023 , Vol. 27 >Issue 3: 178 - 184

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2023.03.015

 

单圈图的Steiner Wiener指数的极值问题

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  • 1. 上海立信会计金融学院, 上海 201209
    2. 山东省平阴县实验学校, 山东济南 250400
张杰, E-mail: zhangjie.sjtu@163.com

收稿日期: 2019-09-18

  网络出版日期: 2023-09-14

基金资助

国家自然科学基金(11701372);国家自然科学基金(11801371);上海市自然科学基金(16ZR1422400);上海市"人才发展资金"(2018071);上海市"扬帆计划"(19YF1435500)

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Extremal problems for Steiner Wiener index of unicyclic graphs

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  • 1. Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
    2. Pingyin Experimental School, Jinan 250400, Shandong, China

Received date: 2019-09-18

  Online published: 2023-09-14

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摘要

Wiener指数作为化学图论中的一个重要的化学指标, 是连通图的任意两个顶点的距离之和。Steiner Wiener指数是Wiener指数的一种推广形式, 定义为所有k个顶点的集合S的Steiner距离的和, 其中S的Steiner距离是包含S的最小连通子图的边数。本文研究了具有最小(大)Steiner Wiener指数的单圈图结构。

关键词： Steiner Wiener指数; Steiner距离; 单圈图; Wiener指数

本文引用格式

张杰, 姬燕 . 单圈图的Steiner Wiener指数的极值问题[J]. 运筹学学报, 2023 , 27(3) : 178 -184 . DOI: 10.15960/j.cnki.issn.1007-6093.2023.03.015

Abstract

Wiener index is an important chemical index in chemical graph theory, defined as the sum of distances between all pairs of vertices. A generalization of the Wiener index, called the Steiner Wiener index, takes the sum of the Steiner distances over all sets S of cardinality k. The Steiner distance of vertices in a set S is the minimum size of a connected subgraph that contain these vertices. We consider the extremal problems with respect to the Steiner Wiener index among all unicyclic graphs.

Key words： Steiner Wiener index; Steiner distance; unicyclic graphs; Wiener index

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