{"title":"G × Z_2的对称着色","authors":"Jabulani Phakathi, Yevhen Zelenyuk, Yuliya Zelenyuk","doi":"10.5614/ejgta.2023.11.2.3","DOIUrl":null,"url":null,"abstract":"Let G be a finite group and let r ∈ N . An r -coloring of G is any mapping χ : G → { 1 , . . . , r } . A coloring χ is symmetric if there is g ∈ G such that χ ( gx − 1 g ) = χ ( x ) for every x ∈ G . We show that if f ( r ) is the polynomial representing the number of symmetric r -colorings of G , then the number of symmetric r -colorings of G × Z 2 is f ( r 2 )","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"61 11","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Symmetric colorings of G × Z_2\",\"authors\":\"Jabulani Phakathi, Yevhen Zelenyuk, Yuliya Zelenyuk\",\"doi\":\"10.5614/ejgta.2023.11.2.3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G be a finite group and let r ∈ N . An r -coloring of G is any mapping χ : G → { 1 , . . . , r } . A coloring χ is symmetric if there is g ∈ G such that χ ( gx − 1 g ) = χ ( x ) for every x ∈ G . We show that if f ( r ) is the polynomial representing the number of symmetric r -colorings of G , then the number of symmetric r -colorings of G × Z 2 is f ( r 2 )\",\"PeriodicalId\":43771,\"journal\":{\"name\":\"Electronic Journal of Graph Theory and Applications\",\"volume\":\"61 11\",\"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.2023.11.2.3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Graph Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5614/ejgta.2023.11.2.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Let G be a finite group and let r ∈ N . An r -coloring of G is any mapping χ : G → { 1 , . . . , r } . A coloring χ is symmetric if there is g ∈ G such that χ ( gx − 1 g ) = χ ( x ) for every x ∈ G . We show that if f ( r ) is the polynomial representing the number of symmetric r -colorings of G , then the number of symmetric r -colorings of G × Z 2 is f ( r 2 )
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We publish research articles written in English in all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences.