TY  - JOUR
ID  - Pejman2019
LB  - Pejman2019
AU  - Pejman, S. Batool
AU  - Payrovi, Shiroyeh
AU  - Behtoei, Ali
TI  - Metric dimension of Andrásfai graphs
ST  - Metric dimension of Andrásfai graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 3
SP  - 415
EP  - 423
DO  - https://doi.org/10.7494/OpMath.2019.39.3.415
UR  - https://doi.org/10.7494/OpMath.2019.39.3.415
AB  - 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 \(dim_M(And(k)\square C_n)\).
KW  - resolving set
KW  - metric dimension
KW  - Andrásfai graph
KW  - Cayley graph
KW  - Cartesian product
SN  - 1232-9274
ER  -