METRIC DIMENSION OF ANDRASFAI GRAPHS

A set W subset of V (G) is called a resolving set, if for each pair of distinct vertices u, v is an element of V (G) there exists t is an element of W such that d(u, t) not equal 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 Andrasfai graphs, their complements and And(k)square P-n. Also, we provide upper and lower bounds for dim(M)(And(k)square C-n).