On Mixed Metric Dimension of Rotationally Symmetric Graphs

A vertex u ∈ V(G) resolves (distinguish or recognize) two elements (vertices or edges) v, w ∈ E(G)UV(G) if d
_G
(u, v) ≠ d
_G
(u, w) . A subset L
_m
of 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 L
_m
. The minimum cardinality of a mixed metric generator for G is called the mixed metric dimension and is denoted by dim
_m
(G). In this paper, we studied the mixed metric dimension for three families of graphs D
_n
, A
_n
, and R
_n
, known from the literature. We proved that, for D
_n
the dim
_m
(D
_n
) = dim
_e
(D
_n
) = dim(D
_n
), when n is even, and for An the dim
_m
(A
_n
) = dim
_e
(A
_n
), when n is even and odd. The graph R
_n
has mixed metric dimension 5.