On the Families of Graphs With Unbounded Metric Dimension

A family G of connected graphs is a family with unbounded metric dimension if dim(G) is not constant and depends on the order of graph. In this paper, we compute the metric dimension of the splitting graphs S(P
_n
) and S(C
_n
) of a path and cycle. We prove that the metric dimension of these graphs varies and depends on the number of vertices of the graph.