The K-Size Edge Metric Dimension of Graphs

Abstract

In this paper, a new concept k-size edge resolving set for a connected graph G in the context of resolvability of graphs is defined. Some properties and realizable results on k-size edge resolvability of graphs are studied. The existence of this new parameter in different graphs is investigated, and the k-size edge metric dimension of path, cycle, and complete bipartite graph is computed. It is shown that these families have unbounded k-size edge metric dimension. Furthermore, the k-size edge metric dimension of the graphs Pm □ Pn, Pm □ Cn for m, n ≥ 3 and the generalized Petersen graph is determined. It is shown that these families of graphs have constant k-size edge metric dimension.