{"title":"利用组合Nullstellensatz构造整数幻图","authors":"R. Low, D. Roberts","doi":"10.26493/2590-9770.1401.a6a","DOIUrl":null,"url":null,"abstract":"Let A be a nontrivial abelian group and A* = A \\ {0}. A graph is A-magic if there exists an edge labeling f using elements of A* which induces a constant vertex labeling of the graph. Such a labeling f is called an A-magic labeling and the constant value of the induced vertex labeling is called an A-magic value. In this paper, we use the Combinatorial Nullstellensatz to construct nontrivial classes of ℤp-magic graphs, prime p ≥ 3. For these graphs, some lower bounds on the number of distinct ℤp-magic labelings are also established.","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"32 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Constructing integer-magic graphs via the Combinatorial Nullstellensatz\",\"authors\":\"R. Low, D. Roberts\",\"doi\":\"10.26493/2590-9770.1401.a6a\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let A be a nontrivial abelian group and A* = A \\\\ {0}. A graph is A-magic if there exists an edge labeling f using elements of A* which induces a constant vertex labeling of the graph. Such a labeling f is called an A-magic labeling and the constant value of the induced vertex labeling is called an A-magic value. In this paper, we use the Combinatorial Nullstellensatz to construct nontrivial classes of ℤp-magic graphs, prime p ≥ 3. For these graphs, some lower bounds on the number of distinct ℤp-magic labelings are also established.\",\"PeriodicalId\":236892,\"journal\":{\"name\":\"Art Discret. Appl. Math.\",\"volume\":\"32 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Art Discret. Appl. Math.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26493/2590-9770.1401.a6a\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Art Discret. Appl. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/2590-9770.1401.a6a","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设A是一个非平凡的阿贝尔群,且A* = A \{0}。一个图是A-magic,如果存在一个边标记f,使用A*的元素,它可以引出一个恒定的顶点标记。这样的标记f称为a -magic标记,而诱导顶点标记的常数值称为a -magic值。本文利用组合nullstellensz构造了素数p≥3的p-幻图的非平凡类。对于这些图,还建立了不同的p-幻标记数的下界。
Constructing integer-magic graphs via the Combinatorial Nullstellensatz
Let A be a nontrivial abelian group and A* = A \ {0}. A graph is A-magic if there exists an edge labeling f using elements of A* which induces a constant vertex labeling of the graph. Such a labeling f is called an A-magic labeling and the constant value of the induced vertex labeling is called an A-magic value. In this paper, we use the Combinatorial Nullstellensatz to construct nontrivial classes of ℤp-magic graphs, prime p ≥ 3. For these graphs, some lower bounds on the number of distinct ℤp-magic labelings are also established.