Abstract
For a simple connected graph G = (V, E), a vertex x E V distinguishes two elements (vertices or edges) x(1) is an element of V, y(1) is an element of E &NOTEQUexpressionL; d(x, x(1)) # d(x, y(1)). A subset Qm c V is a mixed metric generator for G, if every two distinct elements (vertices or edges) of G are distinguished by some vertex of Qm. The minimum cardinality of a mixed metric generator for G is called the mixed metric dimension and denoted by dim(m)(G). In this paper, we investigate the mixed metric dimension for different families of ladder networks. Among these families, we consider Mobius ladder, hexagonal Mobius ladder, triangular Mobius ladder network and conclude that all these families have constant-metric, edge metric and mixed metric dimension.