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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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
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Summary: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.
ISSN:1439-8516
1439-7617