Computing the Mixed Metric Dimension of a Generalized Petersen Graph P(n, 2) - Raza, Hassan; Ji, Ying (Frontiers in Physics, 2020)
Let Γ = (V, E) be a connected graph. A vertex i ∈ V recognizes two elements (vertices or edges) j, k ∈ E ∩ V, if dΓ(i, j) ≠ dΓ(i, k). A set S of vertices in a connected graph Γ is a mixed metric generator for Γ if every two distinct elements (vertices or edges) of Γ are recognized by some vertex of S. The smallest cardinality of a mixed metric generator for Γ is called the mixed metric dimension and is denoted by βm. In this paper, the mixed metric dimension of a generalized Petersen graph P(n, 2) is calculated. We established that a generalized Petersen graph P(n, 2) has a mixed metric dimension equivalent to 4 for n ≡ 0, 2(mod4), and, for n ≡ 1, 3(mod4), the mixed metric dimension is 5. We thus determine that each graph of the family of a generalized Petersen graph P(n, 2) has a constant mixed metric dimension. 2010 Mathematics Subject Classification: 05C12, 05C90