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

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....

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Veröffentlicht in:数学学报：英文版 2014 (7), p.1145-1160
1. Verfasser: Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY
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Sprache:eng
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mod
公制
尺寸
常数
广义Petersen图
度量
维度
证明
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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.
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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）
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