Let G be a connected graph and W be a ordered vertices subset on a connected graph . The set W is called resolving set for G if every vertex on graph G has distinct representation of W. A resolving set containing a minimum number of vertices is called resolving set minimum or basis for G and the cardinality of resolving set is the metric dimension on graph G, denoted by dim(G). In the thesis discusses about metric dimensions of shackle operation C3 cycle graph, dim(Shack(C31,C32,…,C3k:v31=v12,v32=v13,…,v3k-1=v1k ))=2 for k>=2 . To proof this results, we was used mathematical induction method.
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