图的赋权邻域坚韧度

doi:10.6040/j.issn.1671-9352.0.2021.330

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (6): 36-43.doi: 10.6040/j.issn.1671-9352.0.2021.330

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图的赋权邻域坚韧度

翁婷婷,魏宗田

西安建筑科技大学理学院, 陕西西安 710055

发布日期:2022-06-10
作者简介:翁婷婷(1997— ),女,硕士研究生,研究方向为图论、组合优化及其应用. E-mail:weng_tt@163.com
基金资助:
国家自然科学基金资助项目(1661066);陕西省自然科学基金资助项目(2016JM1035);青海省自然科学基金资助项目(2017-ZJ-701)

Weighted neighbor toughness of graphs

WENG Ting-ting, WEI Zong-tian

Department of Mathematics, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China

Published:2022-06-10

摘要/Abstract

摘要： 将邻域坚韧度引入赋权图中,提出图的赋权邻域坚韧度概念。在给出一些基本图的赋权邻域坚韧度的基础上,着重研究几类图的赋权邻域坚韧度的极值问题。结果表明,参数值与图的结构、权值大小和赋权方式均有关系,因而能更为准确地刻画网络的抗毁性。

关键词: 网络抗毁性, 赋权图, 赋权邻域坚韧度, 坚韧度

Abstract: Introduced neighbor toughness into the weighted graph, and the concept of weighted neighbor toughness of the graph is proposed. On the basis of giving some basic graphs weighted neighbor toughness, the extreme value problem of weighted neighbor toughness of several types of graphs was focused. The results show that the parameter values are related to the structure of the graph, the size of the weights, and the way of weighting, so the invulnerability of the network can be described more accurately.

Key words: network invulnerability, weighted graph, weighted neighbor toughness, toughness

中图分类号:

O157.5

翁婷婷,魏宗田. 图的赋权邻域坚韧度[J]. 《山东大学学报(理学版)》, 2022, 57(6): 36-43.

WENG Ting-ting, WEI Zong-tian. Weighted neighbor toughness of graphs[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(6): 36-43.

参考文献

[1] 魏宗田,刘勇,杨威,等.网络抗毁性[M]. 西安:西安交通大学出版社, 2015. WEI Zongtian, LIU Yong, YANG Wei, et al. Network invulnerability[M]. Xian: Xian Jiaotong University Press, 2015.
[2] BONDY J A, MURTY U S R. Graph theory with applications[M]. London: Macmillan Education UK, 1976.
[3] BAUER D, BROERSMA H, SCHMEICHEL E. Toughness in graphs: a survey[J]. Graphs and Combinatorics, 2006, 22(1):1-35.
[4] WU S S Y, COZZENS M B. The minimum size of critically m-neighbour-connected graphs[J]. ARS Combinatoria, 1990, 29:149-160.
[5] 杨静婷. 图的邻域坚韧度研究[D]. 西安: 西安建筑科技大学, 2017. YANG Jingting. A study of vertex neighbor toughness of graphs[D]. Xian: Xian University of Architecture and Technology, 2017.
[6] KATONA G Y, VARGA K. Minimally toughness in special graph classes [J]. Discrete Mathematics, 2018. http://arxiv.org/pdf/1802.00055.pdf.
[7] KATONA G Y, SOLTÉSZ D, VARGA K. Properties of minimally t-tough graphs[J]. Discrete Mathematics, 2018. http://arxiv.org/pdf/1604.02746.pdf.
[8] 马永刚. 图的邻域参数研究 [D]. 大连: 大连海事大学, 2007. MA Yonggang. Research on the neighborhood parameters of graphs [D]. Dalian: Dalian Maritime University, 2007.
[9] 张胜贵,李学良,王力工.通信系统抗破坏能力研究[J]. 西北工业大学学报, 2002, 20(1):100-103. ZHANG Shenggui, LI Xueliang, WANG Ligong. Survivability of communication networks[J]. Journal of Northwestern Polytechnical University, 2002, 20(1):100-103.

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图的赋权邻域坚韧度

Weighted neighbor toughness of graphs

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