Total edge irregularity strength of book graphs and double book graphs

L. Ratnasari, S. Wahyuni, Y. Susanti, D. J. E. Palupi
{"title":"Total edge irregularity strength of book graphs and double book graphs","authors":"L. Ratnasari, S. Wahyuni, Y. Susanti, D. J. E. Palupi","doi":"10.1063/1.5139139","DOIUrl":null,"url":null,"abstract":"Let G(V, E) be a finite, simple and undirected graph with a vertex set V and an edge set E. An edge irregular total k-labeling is a map f : V ∪ E → {1, 2, …, k} such that for any two different edges xy and x’y’ in E, ω(xy) ≠ ω(x’y’) where ω(xy) = f(x) + f(y) + f(xy). The minimum k for which the graph G admits an edge irregular total k-labeling is called the total edge irregularity strength of G, denoted by tes(G). In this paper, we show the exact value of the total edge irregularity strength of any book graph of m sides and n sheets Bn(Cm) and of any double book graph of m sides and 2n sheets 2Bn(Cm).Let G(V, E) be a finite, simple and undirected graph with a vertex set V and an edge set E. An edge irregular total k-labeling is a map f : V ∪ E → {1, 2, …, k} such that for any two different edges xy and x’y’ in E, ω(xy) ≠ ω(x’y’) where ω(xy) = f(x) + f(y) + f(xy). The minimum k for which the graph G admits an edge irregular total k-labeling is called the total edge irregularity strength of G, denoted by tes(G). In this paper, we show the exact value of the total edge irregularity strength of any book graph of m sides and n sheets Bn(Cm) and of any double book graph of m sides and 2n sheets 2Bn(Cm).","PeriodicalId":209108,"journal":{"name":"PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations","volume":"144 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/1.5139139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4

Abstract

Let G(V, E) be a finite, simple and undirected graph with a vertex set V and an edge set E. An edge irregular total k-labeling is a map f : V ∪ E → {1, 2, …, k} such that for any two different edges xy and x’y’ in E, ω(xy) ≠ ω(x’y’) where ω(xy) = f(x) + f(y) + f(xy). The minimum k for which the graph G admits an edge irregular total k-labeling is called the total edge irregularity strength of G, denoted by tes(G). In this paper, we show the exact value of the total edge irregularity strength of any book graph of m sides and n sheets Bn(Cm) and of any double book graph of m sides and 2n sheets 2Bn(Cm).Let G(V, E) be a finite, simple and undirected graph with a vertex set V and an edge set E. An edge irregular total k-labeling is a map f : V ∪ E → {1, 2, …, k} such that for any two different edges xy and x’y’ in E, ω(xy) ≠ ω(x’y’) where ω(xy) = f(x) + f(y) + f(xy). The minimum k for which the graph G admits an edge irregular total k-labeling is called the total edge irregularity strength of G, denoted by tes(G). In this paper, we show the exact value of the total edge irregularity strength of any book graph of m sides and n sheets Bn(Cm) and of any double book graph of m sides and 2n sheets 2Bn(Cm).
书形图和双书形图的总边缘不规则强度
设G(V, E)是一个有顶点集V和边集E的有限、简单无向图,一个边不规则全k标记是一个映射f: V∪E→{1,2,…,k},使得对于E中任意两条不同的边xy和x ' y ', ω(xy)≠ω(x ' y '),其中ω(xy) = f(x) + f(y) + f(xy)。图G允许边缘不规则全k标记的最小k称为G的总边缘不规则强度,用tes(G)表示。在本文中,我们给出了任意m边n片的书状图Bn(Cm)和任意m边2n片的双书状图Bn(Cm)的总边缘不规则强度的精确值。设G(V, E)是一个有顶点集V和边集E的有限、简单无向图,一个边不规则全k标记是一个映射f: V∪E→{1,2,…,k},使得对于E中任意两条不同的边xy和x ' y ', ω(xy)≠ω(x ' y '),其中ω(xy) = f(x) + f(y) + f(xy)。图G允许边缘不规则全k标记的最小k称为G的总边缘不规则强度,用tes(G)表示。在本文中,我们给出了任意m边n片的书状图Bn(Cm)和任意m边2n片的双书状图Bn(Cm)的总边缘不规则强度的精确值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信