The dominant edge metric dimension of graphs

For an ordered subset S = { v 1 , …, k } of vertices in a connected graph G and edge e ′ the metric -representation ′= b is vector r ( ′| )=( d ′, ),…, )) where i )=min{ ), )} . A dominant generator for vertex cover such that edges have pairwise different -representations. smallest size called basis The denoted by D m ) dimension. In this paper, concept dimension (DEMD short) introduced its basic properties are studied. Moreover, NP-hardness computing DEMD graphs proved. Furthermore, invariant investigated under some operations at end paper.