无限三角形网格上的最优误差检测开定位控制集

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2023-01-01 DOI:10.7151/dmgt.2374

Devin C. Jean, S. Seo

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引用次数: 10

摘要

设G为图，S⊥V (G)表示安装了“探测器”的顶点子集，每个探测器都能感知其开放邻域中的“入侵者”。v∈v (G)的开放定位码是相邻检测器N(v)∩S的集合，如果每个开放定位码都是唯一且非空，则称集合S为开放定位支配集。本文研究了无限三角形网格上的误差检测开定位控制集问题，给出了一个密度为12的解，并证明了它是最优解。

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Optimal error-detecting open-locating-dominating set on the infinite triangular grid

Let G be a graph and S ⊆ V (G) represent a subset of vertices having installed “detectors,” each of which is capable of sensing an “intruder” in its open-neighborhood. The open-locating-code of v ∈ V (G) is the set of neighboring detectors, N(v) ∩ S. The set S is said to be an open-locatingdominating set if every open-locating-code is unique and non-empty. In this paper we focus on error-detecting open-locating-dominating sets on the infinite triangular grid, present a solution with density 12 , and prove it is optimal.

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来源期刊

Discussiones Mathematicae Graph Theory MATHEMATICS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

53 weeks

期刊介绍： The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.