Computing the Mixed Metric Dimension of a Generalized Petersen GraphP(n, 2)

Let Gamma = (V, E) be a connected graph. A vertexi is an element of Vrecognizes two elements (vertices or edges)j, k is an element of E boolean AND V, ifd(Gamma)(i, j) not equal d(Gamma)(i, k). A setSof vertices in a connected graph Gamma is a mixed metric generator for Gamma if every two distinct elements (vertices or edges) of Gamma are recognized by some vertex ofS. The smallest cardinality of a mixed metric generator for Gamma is called the mixed metric dimension and is denoted by beta(m). In this paper, the mixed metric dimension of a generalized Petersen graphP(n, 2) is calculated. We established that a generalized Petersen graphP(n, 2) has a mixed metric dimension equivalent to 4 forn equivalent to 0, 2(mod4), and, forn equivalent to 1, 3(mod4), the mixed metric dimension is 5. We thus determine that each graph of the family of a generalized Petersen graphP(n, 2) has a constant mixed metric dimension. 2010 Mathematics Subject Classification:05C12, 05C90