On Mixed Metric Dimension of Rotationally Symmetric Graphs
Hassan Raza, Jia‐Bao Liu, Shaojian Qu · IEEE Access · 2019
A vertex u ∈ V(G) resolves (distinguish or recognize) two elements (vertices or edges) v, w ∈ E(G)UV(G) if dG(u, v) ≠ dG(u, w) . A subset Lmof vertices in a connected graph G is called a mixed metric generator for G if every two distinct elements (vertices and edges) of G are resolved by some vertex set of Lm. The minimum cardinality of a mixed metric generator for G is called the mixed metric dimension and is denoted by dimm(G). In this paper, we studied the mixed metric dimension for three families of graphs Dn, An, and Rn, known from the literature. We proved that, for Dnthe dimm(Dn) = dime(Dn) = dim(Dn), when n is even, and for An the dimm(An) = dime(An), when n is even and odd. The graph Rnhas mixed metric dimension 5.