{"title":"On the pebbling numbers of Flower, Blanuša and Watkins snarks","authors":"Matheus Adauto , Celina de Figueiredo , Glenn Hurlbert , Diana Sasaki","doi":"10.1016/j.dam.2024.10.020","DOIUrl":null,"url":null,"abstract":"<div><div>Graph pebbling is a game played on graphs with pebbles on their vertices. A pebbling move removes two pebbles from one vertex and places one pebble on an adjacent vertex. The pebbling number <span><math><mrow><mi>π</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> is the smallest <span><math><mi>t</mi></math></span> so that from any initial configuration of <span><math><mi>t</mi></math></span> pebbles it is possible, after a sequence of pebbling moves, to place a pebble on any given target vertex. In this paper, we provide the first results on the pebbling numbers of snarks. Until now, only the Petersen graph had its pebbling number correctly established, although attempts had been made for the Flower and Watkins snarks.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"361 ","pages":"Pages 336-346"},"PeriodicalIF":1.0000,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X24004566","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
Graph pebbling is a game played on graphs with pebbles on their vertices. A pebbling move removes two pebbles from one vertex and places one pebble on an adjacent vertex. The pebbling number is the smallest so that from any initial configuration of pebbles it is possible, after a sequence of pebbling moves, to place a pebble on any given target vertex. In this paper, we provide the first results on the pebbling numbers of snarks. Until now, only the Petersen graph had its pebbling number correctly established, although attempts had been made for the Flower and Watkins snarks.
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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