THE LOCAL METRIC DIMENSION OF MYCIELSKI'S GRAPH - FAHRI TADJUDDIN (90115012), NUR
An ordered set W is called local metric set of G if every two adjacent vertices in G have different representation to W. The minimum cardinality of local metric set of G is called local metric dimension of G, denoted by lmd(G). For a connected graph G with vertex set V(G)={v_1, v_2,Ã‚Â…,v_n} and edge set E(G), the Mycielski's graph of G, denoted by μ(G), is graph with vertex set V(μ(G))={x_1,Ã‚Â…,x_n,y_1,Ã‚Â…,y_n,z} and edge set {x_i x_j| v_i v_j∈E(G)}∪{x_i y_j| v_i v_j∈E(G)}∪{y_i z| 1≤i≤n}. In this project, we determine the bounds of local metric dimension of Mycielski's graph of connected graph G.