| On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4） |
| |
| 作者姓名： | Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY |
| |
| 作者单位： | Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan |
| |
| 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.
|
| 关 键 词： | 广义Petersen图 尺寸 公制 常数 mod 维度 度量 证明 |
On the constant metric dimension of generalized petersen graphs P(n, 4) |
| |
| Saba NAZ,Muhammad SALMAN,Usman ALI,Imran JAVAID,Syed,Ahtsham-ul-Haq,BOKHARY.On the constant metric dimension of generalized petersen graphs P(n, 4)[J].Acta Mathematica Sinica,2014,30(7):1145-1160. |
| |
| Authors: | Saba Naz Muhammad Salman Usman Ali Imran Javaid Syed Ahtsham-ul-Haq Bokhary |
| |
| Institution: | 1. Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, 60800, Pakistan
|
| |
| Abstract: | 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. |
| |
| Keywords: | Metric dimension constant metric dimension generalized Petersen graphs |
| 本文献已被 CNKI 维普 SpringerLink 等数据库收录！ |
|
