Abstract
The concept of metric dimension of graph could be applied in many graphs, one of them is subdivision graph. A subdivision graph of graph G denoted as S(G) is a graph resulting from graph G by replacing an edge uv with a new vertex w and adding two new edges uw and wv. In this paper, the subdivision graph is called k − subdivision denoted by Sk (G), if the number of edges replaced from graph G is k for 1 ≤ k ≤ |E(G)|, where |E(G)| is the size of graph G. The purpose of this research is to find the metric dimension of subdivision graphs Sk (G), specifically for some special graphs, those are path graph (Pn ), cycle graph (Cn ), complete graph (Kn ), star graph (Sn ), ladder graph (Ln ), book graph (Bn ), wheel graph (Wn ) and fan graph (Fn ).
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