Khilyah Munawaroh, A. I. Kristiana, E. R. Albirri, D. Dafik, R. Adawiyah
{"title":"Unicyclic家庭的局部发病率","authors":"Khilyah Munawaroh, A. I. Kristiana, E. R. Albirri, D. Dafik, R. Adawiyah","doi":"10.25037/cgantjma.v2i2.59","DOIUrl":null,"url":null,"abstract":"In this research is a development of local irregularity vertex coloring of graph. The based on definition, as follows: \\textbf{$l:V(G) \\longrightarrow {\\{1, 2, ..., k}\\}$} is called vertex irregular k-labelling and \\textbf{$w:V(G) \\longrightarrow N$} where \\textbf{$w(u) = \\varSigma_{ v \\in N(u)}l(v)$}, $w$ is called local irregularity vertex coloring. A condition for $w$ to be a local irregularity vertex coloring, If \\textit{opt$(l)$ = min\\{maks$(li); li$, vertex labelling function}, and for every \\textbf{$u,v\\in E(G),w(u)\\ne w(v)$}. The chromatic number local irregularity vertex coloring is denoted by $\\chi_{lis}(G)$. In this paper, the researchers will discuss of local irregularity vertex coloring of related unicyclic graphs and we have found the exact value of their chromatic number local irregularity, namely cricket graph, net graph, tadpole graph, \\textit{peach} graph, and bull graph.","PeriodicalId":305608,"journal":{"name":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","volume":"166 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Pewarnaan Titik Ketakteraturan Lokal pada Keluarga Graf Unicyclic\",\"authors\":\"Khilyah Munawaroh, A. I. Kristiana, E. R. Albirri, D. Dafik, R. Adawiyah\",\"doi\":\"10.25037/cgantjma.v2i2.59\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this research is a development of local irregularity vertex coloring of graph. The based on definition, as follows: \\\\textbf{$l:V(G) \\\\longrightarrow {\\\\{1, 2, ..., k}\\\\}$} is called vertex irregular k-labelling and \\\\textbf{$w:V(G) \\\\longrightarrow N$} where \\\\textbf{$w(u) = \\\\varSigma_{ v \\\\in N(u)}l(v)$}, $w$ is called local irregularity vertex coloring. A condition for $w$ to be a local irregularity vertex coloring, If \\\\textit{opt$(l)$ = min\\\\{maks$(li); li$, vertex labelling function}, and for every \\\\textbf{$u,v\\\\in E(G),w(u)\\\\ne w(v)$}. The chromatic number local irregularity vertex coloring is denoted by $\\\\chi_{lis}(G)$. In this paper, the researchers will discuss of local irregularity vertex coloring of related unicyclic graphs and we have found the exact value of their chromatic number local irregularity, namely cricket graph, net graph, tadpole graph, \\\\textit{peach} graph, and bull graph.\",\"PeriodicalId\":305608,\"journal\":{\"name\":\"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS\",\"volume\":\"166 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.25037/cgantjma.v2i2.59\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.25037/cgantjma.v2i2.59","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Pewarnaan Titik Ketakteraturan Lokal pada Keluarga Graf Unicyclic
In this research is a development of local irregularity vertex coloring of graph. The based on definition, as follows: \textbf{$l:V(G) \longrightarrow {\{1, 2, ..., k}\}$} is called vertex irregular k-labelling and \textbf{$w:V(G) \longrightarrow N$} where \textbf{$w(u) = \varSigma_{ v \in N(u)}l(v)$}, $w$ is called local irregularity vertex coloring. A condition for $w$ to be a local irregularity vertex coloring, If \textit{opt$(l)$ = min\{maks$(li); li$, vertex labelling function}, and for every \textbf{$u,v\in E(G),w(u)\ne w(v)$}. The chromatic number local irregularity vertex coloring is denoted by $\chi_{lis}(G)$. In this paper, the researchers will discuss of local irregularity vertex coloring of related unicyclic graphs and we have found the exact value of their chromatic number local irregularity, namely cricket graph, net graph, tadpole graph, \textit{peach} graph, and bull graph.