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Adawiyah, R; Dafik; Alfarisi, R; Prihandini, R M; Agustin, I H; Venkatachalam, M
Journal of physics. Conference series, 05/2020, Volume: 1543, Issue: 1Journal Article
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 S⊂V is an edge metric generator for G if for any two edges e1,e2∈E there is a vertex k∈S such that dG(k,e1≠dG(k,e2)). 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 r(xk|S)≠r(yk|S) 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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