{"title":"独立部分支配","authors":"L. PhiloNithya, Joseph Varghese Kureethara","doi":"10.4067/s0719-06462021000300411","DOIUrl":null,"url":null,"abstract":"For p ∈ (0 , 1] , a set S ⊆ V is said to p -dominate or partially dominate a graph G = ( V, E ) if | N [ S ] | | V | ≥ p . The minimum cardinality among all p -dominating sets is called the p -domination number and it is denoted by γ p ( G ) . Analogously, the independent partial domination ( i p ( G ) ) is introduced and studied here independently and in relation with the classical domination. Further, the partial independent set and the partial independence number β p ( G ) are defined and some of their properties are pre-sented. Finally, the partial domination chain is established as γ p ( G ) ≤ i p ( G ) ≤ β p ( G ) ≤ Γ p ( G ) . ,","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Independent partial domination\",\"authors\":\"L. PhiloNithya, Joseph Varghese Kureethara\",\"doi\":\"10.4067/s0719-06462021000300411\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For p ∈ (0 , 1] , a set S ⊆ V is said to p -dominate or partially dominate a graph G = ( V, E ) if | N [ S ] | | V | ≥ p . The minimum cardinality among all p -dominating sets is called the p -domination number and it is denoted by γ p ( G ) . Analogously, the independent partial domination ( i p ( G ) ) is introduced and studied here independently and in relation with the classical domination. Further, the partial independent set and the partial independence number β p ( G ) are defined and some of their properties are pre-sented. Finally, the partial domination chain is established as γ p ( G ) ≤ i p ( G ) ≤ β p ( G ) ≤ Γ p ( G ) . ,\",\"PeriodicalId\":36416,\"journal\":{\"name\":\"Cubo\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cubo\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4067/s0719-06462021000300411\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cubo","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4067/s0719-06462021000300411","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
摘要
对于p∈(0,1)，若| N [S] | | V |≥p，则集S⊥V p -支配或部分支配图G = (V, E)。所有p -支配集的最小基数称为p -支配数，用γ p (G)表示。同样地，独立部分支配(pi (G))在这里被独立地引入和研究，并与经典支配相关。进一步，定义了偏独立集和偏独立数β p (G)，并给出了它们的一些性质。最后，建立了γ p (G)≤i p (G)≤β p (G)≤Γ p (G)的部分支配链。，
For p ∈ (0 , 1] , a set S ⊆ V is said to p -dominate or partially dominate a graph G = ( V, E ) if | N [ S ] | | V | ≥ p . The minimum cardinality among all p -dominating sets is called the p -domination number and it is denoted by γ p ( G ) . Analogously, the independent partial domination ( i p ( G ) ) is introduced and studied here independently and in relation with the classical domination. Further, the partial independent set and the partial independence number β p ( G ) are defined and some of their properties are pre-sented. Finally, the partial domination chain is established as γ p ( G ) ≤ i p ( G ) ≤ β p ( G ) ≤ Γ p ( G ) . ,
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