On the fault-tolerant metric dimension of convex polytopes

被引：74
|
作者：
Raza, Hassan [1 ]
Hayat, Sakander [2 ]
Pan, Xiang-Feng [1 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei 230601, Anhui, Peoples R China
[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 339卷
关键词：
Metric dimension; Fault-tolerant metric dimension; Convex polytopes; MULTIPLICATIVE ZAGREB INDEXES; TOPOLOGICAL INDEXES; GRAPHS; NETWORKS; FAMILIES; VERTICES; NUMBER; BOUNDS;
D O I：
10.1016/j.amc.2018.07.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A convex polytopes is a polytope that is also a convex set of points in the n-dimensional Euclidean space R-n. By preserving the same adjacency relation between vertices of a convex polytope, its graph is constructed. The metric dimension problem has been extensively studied for convex polytopes and other families of graphs. In this paper, we study the fault-tolerant metric dimension problem for convex polytopes. By using a relation between resolving sets and fault-tolerant resolving sets of graphs, we prove that certain infinite families of convex polytopes are the families of graphs with constant fault-tolerant metric dimension. We conclude the paper with some open problems. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：172 / 185
页数：14
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