The local edge metric dimension of graph

• Published in: Journal of physics. Conference series 2020-05, Vol.1543 (1), p.12009
• Main Authors: Adawiyah, R, Dafik, Alfarisi, R, Prihandini, R M, Agustin, I H, Venkatachalam, M
• Format: Article
• Language: English
• Subjects: Graph theory
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1543/1/012009

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.