{"title":"Induced H-packing k-partition of graphs","authors":"S. Raja, I. Rajasingh, Antony Xavier","doi":"10.1080/23799927.2020.1871418","DOIUrl":null,"url":null,"abstract":"ABSTRACT The minimum induced H-packing k-partition number is denoted by . The induced H-packing k-partition number denoted by is defined as where the minimum is taken over all H-packings of G. In this paper, we obtain the induced -packing k-partition number for trees, slim trees, split graphs, complete bipartite graphs, grids and circulant graphs. We also deal with networks having perfect -packing where is a claw on four vertices. We prove that an induced -packing k-partition problem is NP-Complete. Further we prove that the induced -packing k-partition number of is 2 for all hypercube networks with perfect -packing and prove that for all locally twisted cubes with perfect -packing.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computer Mathematics: Computer Systems Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/23799927.2020.1871418","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 1
Abstract
ABSTRACT The minimum induced H-packing k-partition number is denoted by . The induced H-packing k-partition number denoted by is defined as where the minimum is taken over all H-packings of G. In this paper, we obtain the induced -packing k-partition number for trees, slim trees, split graphs, complete bipartite graphs, grids and circulant graphs. We also deal with networks having perfect -packing where is a claw on four vertices. We prove that an induced -packing k-partition problem is NP-Complete. Further we prove that the induced -packing k-partition number of is 2 for all hypercube networks with perfect -packing and prove that for all locally twisted cubes with perfect -packing.
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