{"title":"双图日冕中的公平迂回支配：优化 CCTV 摄像机安装，实现高效监控","authors":"D. J. Ebenezer, J. X. Parthipan","doi":"10.3329/jsr.v16i1.67723","DOIUrl":null,"url":null,"abstract":"The objective of our research is to analyze the properties of FDD sets in the corona of two graphs and explore their practical application in CCTV camera installation. A set F ⊆ V(G) is considered to be a Fair Detour Dominating set (FDD-set) if it is detour dominating and the number of neighbors within set F is the same for any pair of vertices outside of F. Among these FDD sets, the fγd-set refers to the FDD-set with the smallest number of vertices, and its order defines the Fair Detour Domination number (fγd (G)). We have established that for any arbitrary graphs G1 and G2, fγd (G1 o G2) = |V(G1) iff fd(G2) = 1 we have determined the fγd number of corona products of any connected graph G with the path graph as well as the cycle graph. We also characterized FDD sets in the corona product of two connected graphs and provided a thorough description of how FDD sets can be used in optimizing CCTV camera installation for efficient surveillance.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fair Detour Domination in the Corona of Two Graphs: Optimizing CCTV Camera Installation for Efficient Surveillance\",\"authors\":\"D. J. Ebenezer, J. X. Parthipan\",\"doi\":\"10.3329/jsr.v16i1.67723\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The objective of our research is to analyze the properties of FDD sets in the corona of two graphs and explore their practical application in CCTV camera installation. A set F ⊆ V(G) is considered to be a Fair Detour Dominating set (FDD-set) if it is detour dominating and the number of neighbors within set F is the same for any pair of vertices outside of F. Among these FDD sets, the fγd-set refers to the FDD-set with the smallest number of vertices, and its order defines the Fair Detour Domination number (fγd (G)). We have established that for any arbitrary graphs G1 and G2, fγd (G1 o G2) = |V(G1) iff fd(G2) = 1 we have determined the fγd number of corona products of any connected graph G with the path graph as well as the cycle graph. We also characterized FDD sets in the corona product of two connected graphs and provided a thorough description of how FDD sets can be used in optimizing CCTV camera installation for efficient surveillance.\",\"PeriodicalId\":16984,\"journal\":{\"name\":\"JOURNAL OF SCIENTIFIC RESEARCH\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"JOURNAL OF SCIENTIFIC RESEARCH\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3329/jsr.v16i1.67723\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"JOURNAL OF SCIENTIFIC RESEARCH","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3329/jsr.v16i1.67723","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们的研究目的是分析两图日冕中公平迂回集的性质，并探索其在闭路电视摄像机安装中的实际应用。如果一个集合 F ⊆ V(G)具有迂回支配性，且集合 F 内的邻接数对于 F 外的任意一对顶点都相同，则该集合 F ⊆ V(G)被认为是公平迂回支配集（FDD 集）。我们已经确定，对于任意图 G1 和 G2，如果 fd(G2) = 1，则 fγd (G1 o G2) = |V(G1) 我们还确定了任意连通图 G 与路径图以及循环图的日冕积的 fγd 数。我们还确定了两个连通图的日冕积中的 FDD 集的特征，并全面描述了如何将 FDD 集用于优化 CCTV 摄像机安装以实现高效监控。
Fair Detour Domination in the Corona of Two Graphs: Optimizing CCTV Camera Installation for Efficient Surveillance
The objective of our research is to analyze the properties of FDD sets in the corona of two graphs and explore their practical application in CCTV camera installation. A set F ⊆ V(G) is considered to be a Fair Detour Dominating set (FDD-set) if it is detour dominating and the number of neighbors within set F is the same for any pair of vertices outside of F. Among these FDD sets, the fγd-set refers to the FDD-set with the smallest number of vertices, and its order defines the Fair Detour Domination number (fγd (G)). We have established that for any arbitrary graphs G1 and G2, fγd (G1 o G2) = |V(G1) iff fd(G2) = 1 we have determined the fγd number of corona products of any connected graph G with the path graph as well as the cycle graph. We also characterized FDD sets in the corona product of two connected graphs and provided a thorough description of how FDD sets can be used in optimizing CCTV camera installation for efficient surveillance.
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