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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 = {q 1 , q 2 , . . . , q k } 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, q 1 ), r(a, q 2 ), . . . , r(a, q k )), 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 T n 1, t and T n 1, 2, t , respectively is discussed and proved that it is constant.

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Due to the immense applications of interconnection networks, various new networks are designed and extensively used in computer sciences and engineering fields. Networks can be expressed in the form of graphs, where node become vertex and links between nodes are called edges. To obtain the exact location of a specific node which is unique from all the nodes, several nodes are selected this is called locating/resolving set. Minimum number of nodes in the locating set is called locating number. In this article, we find the exact value of locating number of newly designed hexagonal Möbius ladder network.