广义冠状图的直径度量维数
The Diametral Metric Dimension of Generalized Corona Graph
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中文总结 AI 辅助
本研究定义并求解广义冠状图的直径度量维数，发现其取决于主图直径与分支图度量维数，为基础设施规划提供理论支撑。
中文摘要 AI 辅助
本研究探讨了广义冠状图的直径度量维数，其中主图为连通图，分支图构成一个连通图序列。直径度量维数的概念是度量维数概念的扩展，要求分辨集包含所有直径顶点。为确定广义冠状图的直径度量维数，首先需识别图中每个顶点的距离以及图的直径集。随后，确定包含直径集的分辨集。结果表明，广义冠状图的直径度量维数取决于主图的直径以及序列中各图的度量维数。这些概念为基础设施规划中的分辨结构提供了理论见解，并激励对其他图族和图运算的进一步研究。
英文摘要
This study investigates the diametral metric dimension of generalized corona graphs, where the main graph is connected graph and the branch graphs form a sequence of connected graphs. The concept of diametral metric dimension is an extension of the metric dimension concept, requiring the resolving set to contain all diametral vertices. To determine the diametral metric dimension of a generalized corona graph, one must first identify the distance of each vertex in the graph and the graph's diametral set. Subsequently, a resolving set containing the diametral set is determined. The results show that the diametral metric dimension of the generalized corona graph depends on the diameter of the main graph and the metric dimensions of the graphs in the sequence. These concepts provide theoretical insights into resolving structures in the planning infrastructure and motivate further studies on other graph families and graph operations.
发表机构
- Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga（艾尔朗加大学科学与技术学院数学系）
- Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia（马来西亚理工大学理学院数学科学系）
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