On the Edge Metric Dimension of Different Families of Mobius Networks

For an ordered subset Q(e) of vertices in a simple connected graph G, a vertex x is an element of V distinguishes two edges e(1) ,e(2) is an element of E, if d (x, e(1)) # d (x, e(2)). A subset Q(e) having minimum vertices is called an edge metric generator for G, if every two distinct edges of G are distinguished by some vertex of Q(e). The minimum cardinality of an edge metric generator for G is called the edge metric dimension, and it is denoted by dim(e) (G). In this paper, we study the edge resolvability parameter for different families of Mobius ladder networks and we find the exact edge metric dimension of triangular, square, and hexagonal Mobius ladder networks.