The Local Metric Dimension of k-Multilevel Corona of Path, Complete and Cycle Graphs

For an ordered set W={w_1,w_2,…,w_n } of n distinct vertices in a nontrivial connected graph G, the representation of a vertex v of G with respect to W is the n- vector r(v│W)=(d(v,w_1 ),d(v,w_2 ),…,d(v,w_n )). W is a local metric set of G if r(u│W)=r(v│W) for every pair of adjacent vertices u,v in G. Local metric set with minimum cardinality is called local metric basis of G and its cardinality is the local metric dimension of G and denoted by lmd(G). In this paper, we determine the local metric dimension of k-multilevel corona of path, complete, and cycle graphs.