图的广义p-邻域完整度

doi:10.6040/j.issn.1671-9352.0.2021.445

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (10): 72-78.doi: 10.6040/j.issn.1671-9352.0.2021.445

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图的广义p-邻域完整度

崔晨,魏宗田

西安建筑科技大学理学院, 陕西西安 710055

发布日期:2022-10-06
作者简介:崔晨(1996— ),女,硕士研究生,研究方向为图论、组合优化及其应用. E-mail:cc597946987@sina.com
基金资助:
国家自然科学基金资助项目(61902304)

General p-neighbor integrity of graphs

CUI Chen, WEI Zong-tian

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

Published:2022-10-06

摘要/Abstract

摘要： 当网络中一个节点失效后,邻点受其影响也以某个概率p失效。基于此,提出图的广义p-邻域完整度的概念,将完整度与邻域完整度统一起来。通过参数值的计算、与失效概率p的关系分析以及若干同阶图的比较,表明该参数能够更精确地度量网络抗毁性。

关键词: 网络抗毁性, 完整度, 邻域完整度, 失效概率, 广义p-邻域完整度

Abstract: In networks, a failed vertex will lead to its neighborhood fail with a certain probability p. Based on this, the concept of general p-neighbor integrity of graphs is proposed, and therefore the concept of integrity and neighbor integrity are unified by the failure probability. Through the parameter calculation of parameter values, the analysis of the relationship with failure probability p and the parameter value comparison of several graphs with the same order, it is shown that this parameter can measure network invulnerability more accurately.

Key words: network invulnerability, integrity, vertex-neighbor integrity, failure probability, general p-neighbor integrity

中图分类号:

O157.5

崔晨,魏宗田. 图的广义p-邻域完整度[J]. 《山东大学学报(理学版)》, 2022, 57(10): 72-78.

CUI Chen, WEI Zong-tian. General p-neighbor integrity of graphs[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 72-78.

参考文献

[1] JUNG H A. On a class of posets and the corresponding comparability graphs[J]. Journal of Combinatorial Theory. Series B, 1978, 24(2):125-133.
[2] BAREFOOT C A, ENTRINGER R, SWART H. Vulnerability in graphs-a comparative survey[J]. J Combin Math Combin Comput, 1987, 1:13-22.
[3] COZZENS M. Stability measures and data fusion networks[J]. Graph Theory Notes of New York, 1994, X X VI: 8-14.
[4] COZZENS M, WU S SY. Vertex-neighbor-integrity of trees[J]. ARS Combinatoria, 1996, 43:169-180.
[5] WEI Zongtian, ZHANG Shenggui. Vertex-neighbor-integrity of composition graphs of paths[J]. ARS Combinatoria, 2008, 86:349-361.
[6] 杨雪. 图的广义p-邻域抗毁性参数研究[D]. 西安: 西安建筑科技大学, 2021. YANG Xue. A study of the general p-neighbor invulnerability parameters of graphs[D]. Xian: Xian University of Architecture and Technology, 2021.
[7] BONDY J A, MURTY U S R. Graph theory[M]. London: Springer London, 2008. doi:10.1007/978-1-84628-970-5.
[8] 刘勇, 杨淑姝, 魏宗田, 等. 图的弱毁裂度与网络抗毁性[J]. 工程数学学报, 2021, 38(3):362-368. LIU Yong, YANG Shushu, WEI Zongtian, et al. The weak rupture degree of graphs and the network invulnerability[J]. Chinese Journal of Engineering Mathematics, 2021, 38(3):362-368.
[9] 姚焱. 两类图参数的极值问题研究[D]. 淄博: 山东理工大学, 2020. YAO Yan. Study on extremal problems of two classes of graph parameters[D]. Zibo: Shandong University of Technology, 2020.
[10] LI Y K, DU M Z, LI H Y, et al. Edge rupture degree of graphs[J]. International Journal of Foundations of Computer Science, 2017, 28(8):993-1006.

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图的广义p-邻域完整度

General p-neighbor integrity of graphs

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