{"title":"无限三角形网格上的最优误差检测开定位控制集","authors":"Devin C. Jean, S. Seo","doi":"10.7151/dmgt.2374","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Optimal error-detecting open-locating-dominating set on the infinite triangular grid\",\"authors\":\"Devin C. Jean, S. Seo\",\"doi\":\"10.7151/dmgt.2374\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":48875,\"journal\":{\"name\":\"Discussiones Mathematicae Graph Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discussiones Mathematicae Graph Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7151/dmgt.2374\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discussiones Mathematicae Graph Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7151/dmgt.2374","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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