2015/08/14 by Kuziak, Dorota, Peterin, Iztok, Yero, Ismael G. · 2 citations
#05C12 #05C76 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1508.03447
Given a connected graph G, a vertex w∈ 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.