{"title":"广义Petersen图P（N,2）的定位色数界","authors":"Redha Sakri , Boualem Slimi","doi":"10.1016/j.exco.2025.100183","DOIUrl":null,"url":null,"abstract":"<div><div>The concept of the locating-chromatic number for graphs was introduced by Chartrand et al. (2002). Recently, Sakri and Abbas (2024), presented the locating-chromatic number of generalized Petersen graphs <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> when <span><math><mrow><mi>n</mi><mo>≤</mo><mn>12</mn></mrow></math></span>. In this paper, We determine a lower and upper bound for the locating chromatic number of generalized Petersen graphs <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> when <span><math><mi>n</mi></math></span> even and <span><math><mrow><mi>n</mi><mo>≥</mo><mn>14</mn></mrow></math></span>.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"7 ","pages":"Article 100183"},"PeriodicalIF":0.0000,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The bound on the locating-chromatic number for a generalized Petersen graphs P(N,2)\",\"authors\":\"Redha Sakri , Boualem Slimi\",\"doi\":\"10.1016/j.exco.2025.100183\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The concept of the locating-chromatic number for graphs was introduced by Chartrand et al. (2002). Recently, Sakri and Abbas (2024), presented the locating-chromatic number of generalized Petersen graphs <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> when <span><math><mrow><mi>n</mi><mo>≤</mo><mn>12</mn></mrow></math></span>. In this paper, We determine a lower and upper bound for the locating chromatic number of generalized Petersen graphs <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> when <span><math><mi>n</mi></math></span> even and <span><math><mrow><mi>n</mi><mo>≥</mo><mn>14</mn></mrow></math></span>.</div></div>\",\"PeriodicalId\":100517,\"journal\":{\"name\":\"Examples and Counterexamples\",\"volume\":\"7 \",\"pages\":\"Article 100183\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2025-03-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Examples and Counterexamples\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666657X25000102\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Examples and Counterexamples","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666657X25000102","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
图的定位色数概念是由Chartrand et al.（2002）提出的。最近，Sakri和Abbas（2024）给出了n≤12时广义Petersen图P（n,k）的定位色数。本文确定了广义Petersen图P（n,2）在n为偶数且n≥14时的色数定位的下界和上界。
The bound on the locating-chromatic number for a generalized Petersen graphs P(N,2)
The concept of the locating-chromatic number for graphs was introduced by Chartrand et al. (2002). Recently, Sakri and Abbas (2024), presented the locating-chromatic number of generalized Petersen graphs when . In this paper, We determine a lower and upper bound for the locating chromatic number of generalized Petersen graphs when even and .
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