{"title":"车轮图和舵机图的局部反幻顶点着色","authors":"F. F. Hadiputra, D. R. Silaban, T. Maryati","doi":"10.5220/0010138400002775","DOIUrl":null,"url":null,"abstract":": Let 𝜒(cid:4666)𝐺(cid:4667) be a chromatic number of vertex coloring of a graph G. A bijection 𝑓: 𝐸 → (cid:4668)1,2,3, … ,|𝐸(cid:4666)𝐺(cid:4667)|(cid:4669) is called local antimagic vertex coloring if for any adjacent vertices do not share the same weight, where the weight of a vertex in 𝐺 is the sum of the label of edges incident to it. We denote the minimum number of distinct weight of vertices in 𝐺 so that the graph 𝐺 admits a local antimagic vertex coloring as 𝜒 (cid:3039)(cid:3028) (cid:4666)𝐺(cid:4667) . In this study, we established the missing value of 𝜒 (cid:3039)(cid:3028) for a case in wheel graph and 𝜒 (cid:3039)(cid:3028) for helm graph.","PeriodicalId":257157,"journal":{"name":"Proceedings of the 1st International MIPAnet Conference on Science and Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local Antimagic Vertex Coloring of Wheel Graph and Helm Graph\",\"authors\":\"F. F. Hadiputra, D. R. Silaban, T. Maryati\",\"doi\":\"10.5220/0010138400002775\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": Let 𝜒(cid:4666)𝐺(cid:4667) be a chromatic number of vertex coloring of a graph G. A bijection 𝑓: 𝐸 → (cid:4668)1,2,3, … ,|𝐸(cid:4666)𝐺(cid:4667)|(cid:4669) is called local antimagic vertex coloring if for any adjacent vertices do not share the same weight, where the weight of a vertex in 𝐺 is the sum of the label of edges incident to it. We denote the minimum number of distinct weight of vertices in 𝐺 so that the graph 𝐺 admits a local antimagic vertex coloring as 𝜒 (cid:3039)(cid:3028) (cid:4666)𝐺(cid:4667) . In this study, we established the missing value of 𝜒 (cid:3039)(cid:3028) for a case in wheel graph and 𝜒 (cid:3039)(cid:3028) for helm graph.\",\"PeriodicalId\":257157,\"journal\":{\"name\":\"Proceedings of the 1st International MIPAnet Conference on Science and Mathematics\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 1st International MIPAnet Conference on Science and Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5220/0010138400002775\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 1st International MIPAnet Conference on Science and Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5220/0010138400002775","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Local Antimagic Vertex Coloring of Wheel Graph and Helm Graph
: Let 𝜒(cid:4666)𝐺(cid:4667) be a chromatic number of vertex coloring of a graph G. A bijection 𝑓: 𝐸 → (cid:4668)1,2,3, … ,|𝐸(cid:4666)𝐺(cid:4667)|(cid:4669) is called local antimagic vertex coloring if for any adjacent vertices do not share the same weight, where the weight of a vertex in 𝐺 is the sum of the label of edges incident to it. We denote the minimum number of distinct weight of vertices in 𝐺 so that the graph 𝐺 admits a local antimagic vertex coloring as 𝜒 (cid:3039)(cid:3028) (cid:4666)𝐺(cid:4667) . In this study, we established the missing value of 𝜒 (cid:3039)(cid:3028) for a case in wheel graph and 𝜒 (cid:3039)(cid:3028) for helm graph.
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