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For a simple connected graph G=(V,E), an ordered set W⊆V, is called a resolving set of G if for every pair of two distinct vertices u and v, there is an element w in W such that d(u,w)≠d(v,w). A metric basis of G is a resolving set of G with minimum cardinality. The metric dimension of G is the cardinality of a metric basis and it is denoted by β(G). In this article, we determine the metric dimension of power of finite paths and characterize all metric bases for the same.

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Metric Dimension of a simple connected graph is the minimum number of vertices those are used to identify each vertex of the graph uniquely using distance code. In this paper, we determine metric dimension of ideal-intersection graph for the ring Z n , where n being a positive integer.