Let G be any connected graph of order n, X = { x1, x2, ..., xk} be an order set ofvertices and y a vertex in G. The representation of y with respect to X is theordered k-tuple r(v|X) = (d(y, x1), d(y, x2), ..., d(y, xk)), where d(u, v) represents thedistance between the vertices u and v. X is called a local resolving set of G ifevery two adjacent vertices u and v in G satisfy r(u|X) ? r(v|X). A minimumlocal resolving set for G is a local basis of G . A local dimension for G, diml(G), isthe cardinality of vertices in a local basis for G. In this article, we study anddetermine general results of local metric dimensions of edge-corona of graphs.
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