On the Metric Dimension of Generalized Petersen Graphs

A family of connected graphs G is said to be a family with constant metric dimension if its metric dimension is finite and does not depend upon the choice of G in G. In this paper, we study the metric dimension of the generalized Petersen graphs P (n, m) for n = 2m + 1 and m ≥ 1 and give partial answer of the question raised in [9]: Is P (n, m) for n ≥ 7 and 3 ≤ m ≤ bn−1 2 c, a family of graphs with constant metric dimension? We prove that the generalized Petersen graphs P (n, m) with n = 2m + 1 have metric dimension 3 for every m ≥ 2.