{"title":"一些阴影距离图的析取全支配","authors":"C. Çiftçi","doi":"10.33401/fujma.790046","DOIUrl":null,"url":null,"abstract":"Let $ G $ be a graph having vertex set $ V(G) $. For $ S\\subseteq V(G) $, if each vertex is adjacent to a vertex in $ S $ or has at least two vertices in $ S $ at distance two from it, then the set $ S $ is a disjunctive total dominating set of $ G $. The disjunctive total domination number is the minimum cardinality of such a set. In this work, we discuss the disjunctive total domination of shadow distance graphs of some graphs such as cycle, path, star, complete bipartite and wheel graphs.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"51 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Disjunctive Total Domination of Some Shadow Distance Graphs\",\"authors\":\"C. Çiftçi\",\"doi\":\"10.33401/fujma.790046\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $ G $ be a graph having vertex set $ V(G) $. For $ S\\\\subseteq V(G) $, if each vertex is adjacent to a vertex in $ S $ or has at least two vertices in $ S $ at distance two from it, then the set $ S $ is a disjunctive total dominating set of $ G $. The disjunctive total domination number is the minimum cardinality of such a set. In this work, we discuss the disjunctive total domination of shadow distance graphs of some graphs such as cycle, path, star, complete bipartite and wheel graphs.\",\"PeriodicalId\":199091,\"journal\":{\"name\":\"Fundamental Journal of Mathematics and Applications\",\"volume\":\"51 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamental Journal of Mathematics and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33401/fujma.790046\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamental Journal of Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33401/fujma.790046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设$ G $是一个顶点集$ V(G) $的图。对于$ S\subseteq V(G) $,如果每个顶点与$ S $中的一个顶点相邻,或者在$ S $中至少有两个与它的距离为2的顶点,则集合$ S $是$ G $的析取总支配集。析取的总支配数是这样一个集合的最小基数。本文讨论了循环图、路径图、星图、完全二部图和轮图的阴影距离图的析取全支配性。
Disjunctive Total Domination of Some Shadow Distance Graphs
Let $ G $ be a graph having vertex set $ V(G) $. For $ S\subseteq V(G) $, if each vertex is adjacent to a vertex in $ S $ or has at least two vertices in $ S $ at distance two from it, then the set $ S $ is a disjunctive total dominating set of $ G $. The disjunctive total domination number is the minimum cardinality of such a set. In this work, we discuss the disjunctive total domination of shadow distance graphs of some graphs such as cycle, path, star, complete bipartite and wheel graphs.