{"title":"The dominating partition dimension and locating-chromatic number of graphs","authors":"Muhammad Ridwan, Hilda Assiyatun, Edy Tri Baskoro","doi":"10.5614/ejgta.2023.11.2.10","DOIUrl":null,"url":null,"abstract":"For every graph G , the dominating partition dimension of G is either the same as its partition dimension or one higher than its partition dimension. In this paper, we consider some general connections among these three graph parameters: partition dimension, locating-chromatic number, and dominating partition dimension. We will show that β p ( G )≤ η p ( G )≤ χ L ( G ) for any graph G with at least 3 vertices. Therefore, we will derive properties for which graphs G have η p ( G )= β p ( G ) or η p ( G )= β p ( G )+1 .","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"58 1","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Graph Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5614/ejgta.2023.11.2.10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
For every graph G , the dominating partition dimension of G is either the same as its partition dimension or one higher than its partition dimension. In this paper, we consider some general connections among these three graph parameters: partition dimension, locating-chromatic number, and dominating partition dimension. We will show that β p ( G )≤ η p ( G )≤ χ L ( G ) for any graph G with at least 3 vertices. Therefore, we will derive properties for which graphs G have η p ( G )= β p ( G ) or η p ( G )= β p ( G )+1 .
对于每一个图G, G的主导划分维数要么等于它的划分维数，要么比它的划分维数高一个。本文考虑了图的划分维数、定位色数和主导划分维数这三个参数之间的一般联系。我们将证明β p (G)≤η p (G)≤χ L (G)对于任何至少有3个顶点的图G。因此，我们将推导出图G具有η p (G)= β p (G)或η p (G)= β p (G)+1的性质。
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