几类特殊图的孤立数
Isolation Number of Several Special Graphs
摘要: 图的孤立集是顶点集的子集使得图中减去它的闭领域后剩下部分构成孤立点集，图的孤立数是图中最小孤立集的基数。孤立数相关概念在日常生活中起着重要的作用，如在流行病学中，可以用来评估孤立措施的有效性；在网络安全领域，孤立数的概念可以用于识别和孤立异常行为或潜在的威胁等。本文确定友谊图、风车图、轮图、风筝图以及杠铃图等几类特殊图的孤立数，并讨论平面格子图的孤立数。
Abstract: The isolation set of a graph is a subset of the vertex set such that the remaining part after subtracting its closed neighborhood from the graph constitutes an isolated vertex set, and the isolation number of a graph is the cardinality of the smallest isolated set in the graph. The concept of isolation numbers plays an important role in daily life, such as in epidemiology, where it can be used to evaluate the effectiveness of isolation measures; in the field of cybersecurity, the concept of isolation numbers can be used to identify and isolate abnormal behavior or potential threats. This article determines the isolation numbers of several special types of graphs, such as friendship graphs, windmill graphs, wheel graphs, kite graphs, and barbell graphs, and discusses the isolation numbers of plane grid graphs.
文章引用：阿不都艾再孜·乌不力哈斯木, 买吐肉孜·买司地克. 几类特殊图的孤立数[J]. 应用数学进展, 2025, 14(1): 173-184. https://doi.org/10.12677/aam.2025.141020

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