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....

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
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
Format: Artikel
Sprache:eng
Schlagworte:
mod
公制
尺寸
常数
广义Petersen图
度量
维度
证明
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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