Mixed Metric Dimension of Cartesian Product of Cycle and Path

Abstract

The mixed metric dimension is a recently introduced parameter that measures how a set of vertices can uniquely identify all elements (both vertices and edges) of a graph. A vertex w ∈ V distinguishes two elements x, y ∈ V ∪ E if their distances from w are distinct, i.e., dG(w, x) ≠ dG(w, y). A set S ⊆ V is a mixed metric generator for a connected graph G if every pair of distinct elements in G is distinguished by at least one vertex in S. The minimum cardinality of such a set is the mixed metric dimension of G, denoted by mdim(G). In essence, the selected vertices in S provide a unique representation for every vertex and edge in the graph. In this paper, we determine the mixed metric dimensions for the Cartesian product of a cycle and a path, denoted by Cm□Pn.