Abstract
Given a connected graph G, a vertex \({w \in V(G)}\) distinguishes two different vertices u, v of G if the distances between w and u, and between w and v are different. Moreover, w strongly resolves the pair u, v if there exists some shortest u−w path containing v or some shortest v−w path containing u. A set W of vertices is a (strong) metric generator for G if every pair of vertices of G is (strongly resolved) distinguished by some vertex of W. The smallest cardinality of a (strong) metric generator for G is called the (strong) metric dimension of G. In this article we study the (strong) metric dimension of some families of direct product graphs.
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