Computing metric dimension of certain families of toeplitz graphs

Abstract

The position of a moving point in a connected graph can be identified by computing the distance from the point to a set of sonar stations which have been appropriately situated in the graph. Let Q={q1,q2, ⋯, qk} be an ordered set of vertices of a graph G and a is any vertex in G, then the code/representation of a w.r.t Q is the k-tuple ({r(a,q1), r(a,q2), ⋯, r(a,qk)) , denoted by r(a|Q). If the different vertices of G have the different representations w.r.t Q , then Q is known as a resolving set/locating set. A resolving/locating set having the least number of vertices is the basis for G and the number of vertices in the basis is called metric dimension of G and it is represented as dim(G). In this paper, the metric dimension of Toeplitz graphs generated by two and three parameters denoted by Tn 1,t and Tn 1,2,t , respectively is discussed and proved that it is constant.