Javier Hassan, Abdurajan B. Lintasan, N. H. M. Mohammad
{"title":"Some Properties and Realization Problems Involving Connected Outer-hop Independent Hop Domination in Graphs","authors":"Javier Hassan, Abdurajan B. Lintasan, N. H. M. Mohammad","doi":"10.29020/nybg.ejpam.v16i3.4684","DOIUrl":null,"url":null,"abstract":"In this paper, we construct a realization problems involving connected outer-hop independent hop domination and we determine its connections with other known parameters in graph theory. In particular, given two positive integers a and b with 2 ≤ a ≤ b are realizable as the connected hop domination, connected outer-hop independent hop domination, and connected outer-independent hop domination numbers, respectively, of a connected graph. In addition, we characterize the connected outer-hop independent hop dominating sets in some families of graphs, join and corona of two graphs, and we use these results to derive formulas for the parameters of these graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29020/nybg.ejpam.v16i3.4684","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
In this paper, we construct a realization problems involving connected outer-hop independent hop domination and we determine its connections with other known parameters in graph theory. In particular, given two positive integers a and b with 2 ≤ a ≤ b are realizable as the connected hop domination, connected outer-hop independent hop domination, and connected outer-independent hop domination numbers, respectively, of a connected graph. In addition, we characterize the connected outer-hop independent hop dominating sets in some families of graphs, join and corona of two graphs, and we use these results to derive formulas for the parameters of these graphs.