Abstract
In this paper, we introduce a new notion of graph theory study, namely a local edge metric dimension. It is a natural extension of metric dimension concept. dG (e,v) = min{d(x,v),d(y,v)} is the distance between the vertex v and the edge xy in graph G. A non empty set is an edge metric generator for G if for any two edges there is a vertex such that . The minimum cardinality of edge metric generator for G is called as edge metric dimension of G, denoted by dimE (G). The local edge metric dimension of G, denoted by dimE (G), is a local edge metric generator of G if for every pair xk,ky of adjacent edges of G. Our concern in this paper is investigating some results of local edge metric dimension on some graphs.
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