路和圈的笛卡尔积的全隔离数
Total Isolation Number of the Cartesian Product of Paths and Cycles
DOI: 10.12677/aam.2025.149398, PDF,    国家自然科学基金支持
作者: 赵宇慧：青海师范大学数学与统计学院，青海 西宁；李 贺：山西传媒学院信息工程学院，山西 晋中；张淑敏*：青海师范大学数学与统计学院，青海 西宁；藏语智能信息处理及应用国家重点实验室，青海 西宁
关键词: 部分控制；全隔离数；笛卡尔积；Partial Domination； Total Isolation Number； Cartesian Product
摘要: 设 G=( V,E ) 是一个图且集合 S⊆V ，如果V\N[S]是G的一个独立集，则集合S称作是G的一个隔离集。当S是一个隔离集且G[S]不含孤立点时，集合S称作是G的一个全隔离集。图的全隔离数是图中最小的全隔离集的基数。本文主要研究路和圈的笛卡尔积的全隔离数。
Abstract: Let G=( V,E ) be a graph and S⊆V . The set S is called an isolating set of G if V\N[S] is an independent set of G. When S is an isolating set and G[S] contains no isolated vertices, S is a total isolating set of G. The total isolation number of a graph is the minimum cardinality of a total isolating set in the graph. This paper mainly studies the total isolation number of the Cartesian product of paths and cycles.
文章引用：赵宇慧, 李贺, 张淑敏. 路和圈的笛卡尔积的全隔离数[J]. 应用数学进展, 2025, 14(9): 46-59. https://doi.org/10.12677/aam.2025.149398

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