S. Cichacz, Agnieszka G�rlich, Andrea Semani�ov�-Fe�ov��kov�
{"title":"若干图族距离顶点不规则性强度的上界","authors":"S. Cichacz, Agnieszka G�rlich, Andrea Semani�ov�-Fe�ov��kov�","doi":"10.7494/opmath.2022.42.4.561","DOIUrl":null,"url":null,"abstract":"For a graph \\(G\\) its distance vertex irregularity strength is the smallest integer \\(k\\) for which one can find a labeling \\(f: V(G)\\to \\{1, 2, \\dots, k\\}\\) such that \\[ \\sum_{x\\in N(v)}f(x)\\neq \\sum_{x\\in N(u)}f(x)\\] for all vertices \\(u,v\\) of \\(G\\), where \\(N(v)\\) is the open neighborhood of \\(v\\). In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Upper bounds on distance vertex irregularity strength of some families of graphs\",\"authors\":\"S. Cichacz, Agnieszka G�rlich, Andrea Semani�ov�-Fe�ov��kov�\",\"doi\":\"10.7494/opmath.2022.42.4.561\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a graph \\\\(G\\\\) its distance vertex irregularity strength is the smallest integer \\\\(k\\\\) for which one can find a labeling \\\\(f: V(G)\\\\to \\\\{1, 2, \\\\dots, k\\\\}\\\\) such that \\\\[ \\\\sum_{x\\\\in N(v)}f(x)\\\\neq \\\\sum_{x\\\\in N(u)}f(x)\\\\] for all vertices \\\\(u,v\\\\) of \\\\(G\\\\), where \\\\(N(v)\\\\) is the open neighborhood of \\\\(v\\\\). In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.\",\"PeriodicalId\":45563,\"journal\":{\"name\":\"Opuscula Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Opuscula Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7494/opmath.2022.42.4.561\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Opuscula Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7494/opmath.2022.42.4.561","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Upper bounds on distance vertex irregularity strength of some families of graphs
For a graph \(G\) its distance vertex irregularity strength is the smallest integer \(k\) for which one can find a labeling \(f: V(G)\to \{1, 2, \dots, k\}\) such that \[ \sum_{x\in N(v)}f(x)\neq \sum_{x\in N(u)}f(x)\] for all vertices \(u,v\) of \(G\), where \(N(v)\) is the open neighborhood of \(v\). In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.