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 iV recognizes two elements (vertices or edges) j,kE V, if d_Γ(i,j)≠ d_Γ(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 β_m. In this paper, the mixed metric dimension of generalized Petersen graph P(n,2) is calculated. We established that generalized Petersen graph P(n,2) has a mixed metric dimension equivalent to 4 for n0,2(mod 4), and for n1,3(mod 4) the mixed metric dimension is 5. Thus determining that each graph of the family of generalized Petersen graph P(n,2) has a constant mixed metric dimension.