On the constant metric dimension of generalized petersen graphs P(n, 4)

Abstract

In this paper, we consider the family of generalized Petersen graphs P(n, 4). We prove that the metric dimension of P(n, 4) is 3 when n ≡ 0 (mod 4), and is 4 when n = 4k + 3 (k is even). For n ≡ 1,2 (mod 4) and n = 4k + 3 (k is odd), we prove that the metric dimension of P(n, 4) is bounded above by 4. This shows that each graph of the family of generalized Petersen graphs P(n, 4) has constant metric dimension.