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

On the Constant Metric Dimension of Generalized Petersen Graphs P(n,4)
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摘要 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. 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.
作者 Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY
机构地区 Center for Advanced Studies in Pure and Applied Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第7期1145-1160,共16页 数学学报（英文版）
关键词 Metric dimension constant metric dimension generalized Petersen graphs Metric dimension, constant metric dimension, generalized Petersen graphs
分类号 O157.5 [理学—基础数学] TB911 [机械工程—测试计量技术及仪器]
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Acta Mathematica Sinica,English Series
2014年 第7期

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