{"title":"On a generalization of roman domination with more legions","authors":"Fahimeh Khosh-Ahang Ghasr","doi":"10.1142/s1793830923500040","DOIUrl":null,"url":null,"abstract":"In this note, we generalize the concepts of (perfect) Roman and Italian dominations to (perfect) strong Roman and Roman k-domination for arbitrary positive integer k. These generalizations cover some of previous ones. After some comparison of their domination numbers, as a first study of these concepts, we study the (perfect, strong, perfect strong) Roman k-domination numbers of complete bipartite graphs.","PeriodicalId":45568,"journal":{"name":"Discrete Mathematics Algorithms and Applications","volume":"35 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics Algorithms and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s1793830923500040","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this note, we generalize the concepts of (perfect) Roman and Italian dominations to (perfect) strong Roman and Roman k-domination for arbitrary positive integer k. These generalizations cover some of previous ones. After some comparison of their domination numbers, as a first study of these concepts, we study the (perfect, strong, perfect strong) Roman k-domination numbers of complete bipartite graphs.
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