Determining the edge metric dimension of the generalized Petersen graph P(n, 3)

被引：3
|
作者：
Wang, David G. L. [1 ,2 ,3 ]
Wang, Monica M. Y. [1 ]
Zhang, Shiqiang [4 ]
机构：
[1] Beijing Inst Technol, Sch Math & Stat, Beijing 102400, Peoples R China
[2] Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 102400, Peoples R China
[3] Minist Ind & Informat Technol, Key Lab Math Theory & Computat Informat Secur, Beijing 102400, Peoples R China
[4] Imperial Coll London, Dept Comp, London SW7 2AZ, England
来源：
JOURNAL OF COMBINATORIAL OPTIMIZATION | 2022年 / 43卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Generalized Petersen graph; Metric dimension; Resolving set; Floyd-Warshall algorithm; HAMILTONIAN CYCLES; 2-RAINBOW DOMINATION; CROSSING NUMBER;
D O I：
10.1007/s10878-021-00780-8
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
It is known that the problem of computing the edge dimension of a graph is NP-hard, and that the edge dimension of any generalized Petersen graph P(n, k) is at least 3. We prove that the graph P(n, 3) has edge dimension 4 for n >= 11, by showing semi-combinatorially the nonexistence of an edge resolving set of order 3 and by constructing explicitly an edge resolving set of order 4.
引用
收藏
页码：460 / 496
页数：37
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