邻域度量维二的图

IF 0.5 Q4 MULTIDISCIPLINARY SCIENCES

Journal of Mathematical and Fundamental Sciences Pub Date : 2021-06-10 DOI:10.5614/J.MATH.FUND.SCI.2021.53.1.9

B. Sooryanarayana, Suma Agani Shanmukha

{"title":"邻域度量维二的图","authors":"B. Sooryanarayana, Suma Agani Shanmukha","doi":"10.5614/J.MATH.FUND.SCI.2021.53.1.9","DOIUrl":null,"url":null,"abstract":"A subset S of vertices of a simple connected graph is a neighborhood set (n-set) of G if G is the union of subgraphs of G induced by the closed neighbors of elements in S. Further, a set S is a resolving set of G if for each pair of distinct vertices x, y of G, there is a vertex s ∈ S such that d(s, x) ≠ d(s, y). An n-set that serves as a resolving set for G is called an nr-set of G. The nr-set with least cardinality is called an nr-metric basis of G and its cardinality is called the neighborhood metric dimension of graph G. In this paper, we characterize graphs of neighborhood metric dimension two.","PeriodicalId":16255,"journal":{"name":"Journal of Mathematical and Fundamental Sciences","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Graphs of Neighborhood Metric Dimension Two\",\"authors\":\"B. Sooryanarayana, Suma Agani Shanmukha\",\"doi\":\"10.5614/J.MATH.FUND.SCI.2021.53.1.9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A subset S of vertices of a simple connected graph is a neighborhood set (n-set) of G if G is the union of subgraphs of G induced by the closed neighbors of elements in S. Further, a set S is a resolving set of G if for each pair of distinct vertices x, y of G, there is a vertex s ∈ S such that d(s, x) ≠ d(s, y). An n-set that serves as a resolving set for G is called an nr-set of G. The nr-set with least cardinality is called an nr-metric basis of G and its cardinality is called the neighborhood metric dimension of graph G. In this paper, we characterize graphs of neighborhood metric dimension two.\",\"PeriodicalId\":16255,\"journal\":{\"name\":\"Journal of Mathematical and Fundamental Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-06-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical and Fundamental Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5614/J.MATH.FUND.SCI.2021.53.1.9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical and Fundamental Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5614/J.MATH.FUND.SCI.2021.53.1.9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}

引用次数: 1

摘要

一个简单连通图的顶点子集S是G的邻域集(n集)，如果G是G的子图由S中元素的闭邻归纳而成的并集。更进一步，如果对于G的每一对不同的顶点x, y，存在一个顶点S∈S使得d(S, x)≠d(S)，则集合S是G的解析集，作为G的解析集的n-集合称为G的nr-集合。具有最小基数的nr-集合称为G的nr-度量基，其基数称为图G的邻域度量维数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Graphs of Neighborhood Metric Dimension Two

A subset S of vertices of a simple connected graph is a neighborhood set (n-set) of G if G is the union of subgraphs of G induced by the closed neighbors of elements in S. Further, a set S is a resolving set of G if for each pair of distinct vertices x, y of G, there is a vertex s ∈ S such that d(s, x) ≠ d(s, y). An n-set that serves as a resolving set for G is called an nr-set of G. The nr-set with least cardinality is called an nr-metric basis of G and its cardinality is called the neighborhood metric dimension of graph G. In this paper, we characterize graphs of neighborhood metric dimension two.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Mathematical and Fundamental Sciences MULTIDISCIPLINARY SCIENCES-

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

24 weeks

期刊介绍： Journal of Mathematical and Fundamental Sciences welcomes full research articles in the area of Mathematics and Natural Sciences from the following subject areas: Astronomy, Chemistry, Earth Sciences (Geodesy, Geology, Geophysics, Oceanography, Meteorology), Life Sciences (Agriculture, Biochemistry, Biology, Health Sciences, Medical Sciences, Pharmacy), Mathematics, Physics, and Statistics. New submissions of mathematics articles starting in January 2020 are required to focus on applied mathematics with real relevance to the field of natural sciences. Authors are invited to submit articles that have not been published previously and are not under consideration elsewhere.