On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4）

In this paper, we consider the family of generalized Petersen graphs P（n,4）. We prove that the metric dimension of P（n, 4） is 3 when n = 0 （mod 4）, and is 4 when n = 4k ＋ 3 （k is even）.For n = 1,2 （mod 4） and n = 4k ＋ 3 （k is odd）, we prove that the metric dimension of P（n,4） is bounded above by 4....

Full description

Saved in:
Bibliographic Details
Published in:数学学报：英文版 2014 (7), p.1145-1160
Main Author: Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY
Format: Article
Language:English
Subjects:
mod
公制
尺寸
常数
广义Petersen图
度量
维度
证明
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 1160
container_issue 7
container_start_page 1145
container_title 数学学报：英文版
container_volume
creator Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY
description In this paper, we consider the family of generalized Petersen graphs P（n,4）. We prove that the metric dimension of P（n, 4） is 3 when n = 0 （mod 4）, and is 4 when n = 4k ＋ 3 （k is even）.For n = 1,2 （mod 4） and n = 4k ＋ 3 （k is odd）, we prove that the metric dimension of P（n,4） is bounded above by 4. This shows that each graph of the family of generalized Petersen graphs P（n, 4） has constant metric dimension.
format article
fullrecord <record><control><sourceid>chongqing</sourceid><recordid>TN_cdi_chongqing_primary_49943869</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cqvip_id>49943869</cqvip_id><sourcerecordid>49943869</sourcerecordid><originalsourceid>FETCH-chongqing_primary_499438693</originalsourceid><addsrcrecordid>eNqNyjsOgkAUQNGJ0UT87OHZSwLhOzUqJsZIYU8m-IAx8MCZaXQFuif2xBZsXIDVPcWdMMv1PW5HoRtNf44DN5yzhdZ3xwkC7oQWO10ITI2QdKSNIANnNEoWsJMtkpYdQVdCioRKNPKFN8jQoNJIkCrR1xqycXjTFvxx-KzYrBSNxvWvS7Y57K_J0S7qjqqHpCrvlWyFeuY-574Xh9z75_kCY70-aw</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4）</title><source>ABI/INFORM Global</source><source>Springer Nature:Jisc Collections:Springer Nature Read and Publish 2023-2025: Springer Reading List</source><creator>Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY</creator><creatorcontrib>Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY</creatorcontrib><description>In this paper, we consider the family of generalized Petersen graphs P（n,4）. We prove that the metric dimension of P（n, 4） is 3 when n = 0 （mod 4）, and is 4 when n = 4k ＋ 3 （k is even）.For n = 1,2 （mod 4） and n = 4k ＋ 3 （k is odd）, we prove that the metric dimension of P（n,4） is bounded above by 4. This shows that each graph of the family of generalized Petersen graphs P（n, 4） has constant metric dimension.</description><identifier>ISSN: 1439-8516</identifier><identifier>EISSN: 1439-7617</identifier><language>eng</language><subject>mod ; 公制 ; 尺寸 ; 常数 ; 广义Petersen图 ; 度量 ; 维度 ; 证明</subject><ispartof>数学学报：英文版, 2014 (7), p.1145-1160</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://image.cqvip.com/vip1000/qk/85800X/85800X.jpg</thumbnail><link.rule.ids>314,780,784,4024</link.rule.ids></links><search><creatorcontrib>Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY</creatorcontrib><title>On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4）</title><title>数学学报：英文版</title><addtitle>Acta Mathematica Sinica</addtitle><description>In this paper, we consider the family of generalized Petersen graphs P（n,4）. We prove that the metric dimension of P（n, 4） is 3 when n = 0 （mod 4）, and is 4 when n = 4k ＋ 3 （k is even）.For n = 1,2 （mod 4） and n = 4k ＋ 3 （k is odd）, we prove that the metric dimension of P（n,4） is bounded above by 4. This shows that each graph of the family of generalized Petersen graphs P（n, 4） has constant metric dimension.</description><subject>mod</subject><subject>公制</subject><subject>尺寸</subject><subject>常数</subject><subject>广义Petersen图</subject><subject>度量</subject><subject>维度</subject><subject>证明</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqNyjsOgkAUQNGJ0UT87OHZSwLhOzUqJsZIYU8m-IAx8MCZaXQFuif2xBZsXIDVPcWdMMv1PW5HoRtNf44DN5yzhdZ3xwkC7oQWO10ITI2QdKSNIANnNEoWsJMtkpYdQVdCioRKNPKFN8jQoNJIkCrR1xqycXjTFvxx-KzYrBSNxvWvS7Y57K_J0S7qjqqHpCrvlWyFeuY-574Xh9z75_kCY70-aw</recordid><startdate>2014</startdate><enddate>2014</enddate><creator>Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY</creator><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope></search><sort><creationdate>2014</creationdate><title>On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4）</title><author>Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-chongqing_primary_499438693</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>mod</topic><topic>公制</topic><topic>尺寸</topic><topic>常数</topic><topic>广义Petersen图</topic><topic>度量</topic><topic>维度</topic><topic>证明</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><jtitle>数学学报：英文版</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4）</atitle><jtitle>数学学报：英文版</jtitle><addtitle>Acta Mathematica Sinica</addtitle><date>2014</date><risdate>2014</risdate><issue>7</issue><spage>1145</spage><epage>1160</epage><pages>1145-1160</pages><issn>1439-8516</issn><eissn>1439-7617</eissn><abstract>In this paper, we consider the family of generalized Petersen graphs P（n,4）. We prove that the metric dimension of P（n, 4） is 3 when n = 0 （mod 4）, and is 4 when n = 4k ＋ 3 （k is even）.For n = 1,2 （mod 4） and n = 4k ＋ 3 （k is odd）, we prove that the metric dimension of P（n,4） is bounded above by 4. This shows that each graph of the family of generalized Petersen graphs P（n, 4） has constant metric dimension.</abstract></addata></record>
fulltext fulltext
identifier ISSN: 1439-8516
ispartof 数学学报：英文版, 2014 (7), p.1145-1160
issn 1439-8516
1439-7617
language eng
recordid cdi_chongqing_primary_49943869
source ABI/INFORM Global; Springer Nature:Jisc Collections:Springer Nature Read and Publish 2023-2025: Springer Reading List
subjects mod
公制
尺寸
常数
广义Petersen图
度量
维度
证明
title On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4）
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-20T09%3A43%3A12IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-chongqing&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20Constant%20Metric%20Dimension%20of%20Generalized%20Petersen%20Graphs%20P%EF%BC%88n,%204%EF%BC%89&rft.jtitle=%E6%95%B0%E5%AD%A6%E5%AD%A6%E6%8A%A5%EF%BC%9A%E8%8B%B1%E6%96%87%E7%89%88&rft.au=Saba%20NAZ%20Muhammad%20SALMAN%20Usman%20ALI%20Imran%20JAVAID%20Syed%20Ahtsham-ul-Haq%20BOKHARY&rft.date=2014&rft.issue=7&rft.spage=1145&rft.epage=1160&rft.pages=1145-1160&rft.issn=1439-8516&rft.eissn=1439-7617&rft_id=info:doi/&rft_dat=%3Cchongqing%3E49943869%3C/chongqing%3E%3Cgrp_id%3Ecdi_FETCH-chongqing_primary_499438693%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_cqvip_id=49943869&rfr_iscdi=true