{"title":"广义Petersen图P（n，k）的d-距离着色","authors":"Ramy S. Shaheen, Z. Kanaya, Samar Jakhlab","doi":"10.4236/OJDM.2017.74017","DOIUrl":null,"url":null,"abstract":"A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χd(G). In this paper, we give the exact value of χd(G) (d = 1, 2), for some types of generalized Petersen graphs P(n, k) where k = 1, 2, 3 and arbitrary n.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"07 1","pages":"185-199"},"PeriodicalIF":0.0000,"publicationDate":"2017-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"d-Distance Coloring of Generalized Petersen Graphs P(n, k)\",\"authors\":\"Ramy S. Shaheen, Z. Kanaya, Samar Jakhlab\",\"doi\":\"10.4236/OJDM.2017.74017\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χd(G). In this paper, we give the exact value of χd(G) (d = 1, 2), for some types of generalized Petersen graphs P(n, k) where k = 1, 2, 3 and arbitrary n.\",\"PeriodicalId\":61712,\"journal\":{\"name\":\"离散数学期刊(英文)\",\"volume\":\"07 1\",\"pages\":\"185-199\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"离散数学期刊(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.4236/OJDM.2017.74017\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/OJDM.2017.74017","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
d-Distance Coloring of Generalized Petersen Graphs P(n, k)
A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χd(G). In this paper, we give the exact value of χd(G) (d = 1, 2), for some types of generalized Petersen graphs P(n, k) where k = 1, 2, 3 and arbitrary n.
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