{"title":"Γ-supermagic labeling of products of two cycles with cyclic groups","authors":"D. Froncek","doi":"10.19184/ijc.2023.7.1.3","DOIUrl":null,"url":null,"abstract":"A <em>Γ</em>-supermagic labeling of a graph <em>G</em>=(<em>V,E</em>) is a bijection from <em>E</em> to a group <em>Γ</em> of order |<em>E</em>| such that the sum of labels of all edges incident with any vertex <em>x</em>∈ <em>V</em> is equal to the same element μ ∈ <em>Γ</em>. <br /><br />A <em>Z</em><sub>2mn</sub>-supermagic labeling of the Cartesian product of two cycles, <em>C</em><sub>m</sub> ℺ <em>C</em><sub>n</sub> for every <em>m,n</em> ≥ 3 was found by Froncek, McKeown, McKeown, and McKeown. In this paper we present a <em>Z</em><sub>k</sub>-supermagic labeling of the direct and strong product by cyclic group <em>Z</em><sub>k</sub> for any <em>m,n</em> ≥ 3.","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"30 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indonesian Journal of Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19184/ijc.2023.7.1.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A Γ-supermagic labeling of a graph G=(V,E) is a bijection from E to a group Γ of order |E| such that the sum of labels of all edges incident with any vertex x∈ V is equal to the same element μ ∈ Γ.
A Z2mn-supermagic labeling of the Cartesian product of two cycles, Cm ℺ Cn for every m,n ≥ 3 was found by Froncek, McKeown, McKeown, and McKeown. In this paper we present a Zk-supermagic labeling of the direct and strong product by cyclic group Zk for any m,n ≥ 3.
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