{"title":"太阳图的边缘不规则自反标注及双顶点环和零图的电晕","authors":"I. Setiawan, D. Indriati","doi":"10.19184/IJC.2021.5.1.5","DOIUrl":null,"url":null,"abstract":"<p>Let <em>G</em>(<em>V</em>,<em>E</em>) be a simple and connected graph which set of vertices is <em>V</em> and set of edges is <em>E</em>. Irregular reflexive <em>k</em>-labeling f on <em>G</em>(<em>V</em>,<em>E</em>) is assignment that carries the numbers of integer to elements of graph, such that the positive integer {1,2, 3,...,<em>k</em><sub>e</sub>} assignment to edges of graph and the even positive integer {0,2,4,...,2<em>k</em><sub>v</sub>} assignment to vertices of graph. Then, we called as edge irregular reflexive <em>k</em>-labelling if every edges has different weight with <em>k</em> = max{<em>k</em><sub>e</sub>,2<em>k</em><sub>v</sub>}. Besides that, there is definition of reflexive edge strength of <em>G</em>(<em>V</em>,<em>E</em>) denoted as <em>res</em>(<em>G</em>), that is a minimum <em>k</em> that using for labeling <em>f</em> on <em>G</em>(<em>V</em>,<em>E</em>). This paper will discuss about edge irregular reflexive <em>k</em>-labeling for sun graph and corona of cycle and null graph, denoted by <em>C</em><sub>n</sub> ⨀ <em>N</em><sub>2</sub> and make sure about their reflexive edge strengths.</p>","PeriodicalId":13506,"journal":{"name":"Indonesian Journal of Combinatorics","volume":"4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Edge irregular reflexive labeling on sun graph and corona of cycle and null graph with two vertices\",\"authors\":\"I. Setiawan, D. Indriati\",\"doi\":\"10.19184/IJC.2021.5.1.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <em>G</em>(<em>V</em>,<em>E</em>) be a simple and connected graph which set of vertices is <em>V</em> and set of edges is <em>E</em>. Irregular reflexive <em>k</em>-labeling f on <em>G</em>(<em>V</em>,<em>E</em>) is assignment that carries the numbers of integer to elements of graph, such that the positive integer {1,2, 3,...,<em>k</em><sub>e</sub>} assignment to edges of graph and the even positive integer {0,2,4,...,2<em>k</em><sub>v</sub>} assignment to vertices of graph. Then, we called as edge irregular reflexive <em>k</em>-labelling if every edges has different weight with <em>k</em> = max{<em>k</em><sub>e</sub>,2<em>k</em><sub>v</sub>}. Besides that, there is definition of reflexive edge strength of <em>G</em>(<em>V</em>,<em>E</em>) denoted as <em>res</em>(<em>G</em>), that is a minimum <em>k</em> that using for labeling <em>f</em> on <em>G</em>(<em>V</em>,<em>E</em>). This paper will discuss about edge irregular reflexive <em>k</em>-labeling for sun graph and corona of cycle and null graph, denoted by <em>C</em><sub>n</sub> ⨀ <em>N</em><sub>2</sub> and make sure about their reflexive edge strengths.</p>\",\"PeriodicalId\":13506,\"journal\":{\"name\":\"Indonesian Journal of Combinatorics\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indonesian Journal of Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.19184/IJC.2021.5.1.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indonesian Journal of Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19184/IJC.2021.5.1.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Edge irregular reflexive labeling on sun graph and corona of cycle and null graph with two vertices
Let G(V,E) be a simple and connected graph which set of vertices is V and set of edges is E. Irregular reflexive k-labeling f on G(V,E) is assignment that carries the numbers of integer to elements of graph, such that the positive integer {1,2, 3,...,ke} assignment to edges of graph and the even positive integer {0,2,4,...,2kv} assignment to vertices of graph. Then, we called as edge irregular reflexive k-labelling if every edges has different weight with k = max{ke,2kv}. Besides that, there is definition of reflexive edge strength of G(V,E) denoted as res(G), that is a minimum k that using for labeling f on G(V,E). This paper will discuss about edge irregular reflexive k-labeling for sun graph and corona of cycle and null graph, denoted by Cn ⨀ N2 and make sure about their reflexive edge strengths.