Metric dimension of Andrásfai graphs

Opuscula Mathematica

article

Ali Behtoei¹  S. Batool Pejman¹  Shiroyeh Payrovi¹ 

[1] Imam Khomeini International University, Department of Mathematics, Faculty of Science

关键词: resolving set;    metric dimension;    Andrásfai graph;    Cayley graph;    Cartesian product.;   

DOI  :  10.7494/OpMath.2019.39.3.415

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

A set \(W\subseteq V(G)\) is called a resolving set, if for each pair of distinct vertices \(u,v\in V(G)\) there exists \(t\in W\) such that \(d(u,t)\neq d(v,t)\), where \(d(x,y)\) is the distance between vertices \(x\) and \(y\). The cardinality of a minimum resolving set for \(G\) is called the metric dimension of \(G\) and is denoted by \(\dim_M(G)\). This parameter has many applications in different areas. The problem of finding metric dimension is NP-complete for general graphs but it is determined for trees and some other important families of graphs. In this paper, we determine the exact value of the metric dimension of Andrásfai graphs, their complements and \(And(k)\square P_n\). Also, we provide upper and lower bounds for \(dim_M(And(k)\square C_n)\).

【 授权许可】

CC BY-NC