人链图的意大利支配问题
Italian Domination in Human Chain Graphs
DOI: 10.12677/pm.2026.166163, PDF,    国家自然科学基金支持
作者: 陈岚茜：重庆理工大学数学科学学院，重庆；李 鹏：汉江师范学院数学与统计学院，湖北 十堰
关键词: 意大利支配；人链图；意大利支配数；Italian Domination； Human Chain Graph； Italian Domination Number
摘要: 意大利支配问题是罗马支配问题的一种变形，要求每个未赋值顶点至少邻接两个赋值为1的顶点或至少邻接一个赋值为2的顶点。人链图是一类具有规则结构的特定图类。本文在Meiyanathan等人工作的基础上，研究人链图的意大利支配问题。通过图的结构分解和分类讨论，给出了人链图意大利支配数的表达式，丰富了该类图在意大利支配问题上的研究。
Abstract: Italian domination is a generalization of Roman domination, requiring that every unassigned vertex is adjacent to at least two vertices assigned 1 or at least one vertex assigned 2. A human chain graph is a special class of cactus graphs. Based on the work of Meiyanathan et al., this paper studies the Italian domination problem on human chain graphs. By structural decomposition and case analysis, the exact expression of the Italian domination number for human chain graphs is obtained, which enriches the theoretical results on Italian domination for cactus graphs.
文章引用：陈岚茜, 李鹏. 人链图的意大利支配问题[J]. 理论数学, 2026, 16(6): 131-141. https://doi.org/10.12677/pm.2026.166163

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