{"title":"On rainbow domination of generalized Petersen graphs P(ck,k)","authors":"","doi":"10.1016/j.dam.2024.07.052","DOIUrl":null,"url":null,"abstract":"<div><p>The structure of minimal weight rainbow domination functions of cubic graphs are studied. Based on general observations for cubic graphs, generalized Petersen graphs <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>c</mi><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> are characterized whose 4- and 5-rainbow domination numbers equal the general lower bounds. As <span><math><mi>t</mi></math></span>-rainbow domination of cubic graphs for <span><math><mrow><mi>t</mi><mo>≥</mo><mn>6</mn></mrow></math></span> is trivial, characterizations of such generalized Petersen graphs <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>c</mi><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> are known for all <span><math><mi>t</mi></math></span>-rainbow domination numbers. In addition, new upper bounds for 4- and 5-rainbow domination numbers that are valid for all <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>c</mi><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> are provided.</p></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166218X24003512/pdfft?md5=77096f0be751e76906025c8791c91bf6&pid=1-s2.0-S0166218X24003512-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X24003512","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The structure of minimal weight rainbow domination functions of cubic graphs are studied. Based on general observations for cubic graphs, generalized Petersen graphs are characterized whose 4- and 5-rainbow domination numbers equal the general lower bounds. As -rainbow domination of cubic graphs for is trivial, characterizations of such generalized Petersen graphs are known for all -rainbow domination numbers. In addition, new upper bounds for 4- and 5-rainbow domination numbers that are valid for all are provided.
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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