On resolving perfect dominating number of comb product of special graphs

A set of vertices D ⊆ V(G) is the dominating set of graph G if every vertex on graph G is dominated by dominators. The dominating set of D on graph G is a perfect if every point of a graph G is dominated by exactly one vertex on D. For each vertex υ ∈ V (G), the k-vector r(υ| W) is called the metric code or location W, where W = {w₁,w₂,...,w_k} ⊆ V (G). An ordered set W ⊆ V(G) is called the resolving set of graph G if each vertex u, v ∈ V(G) has a different point representation with respect to the W where r(u|W) ≠ r(υ|W). The ordered set W_rp Ç V (G) is called the resolving perfect dominating set on graph G if W_rp is the resolving set and perfect dominating set of graph G. The minimum cardinality of the resolving perfect dominating set is called the resolving perfect dominating number which is denoted by γ_rpG. In this study, we analyzed the resolving perfect dominating number of comb product operations between two connected graphs, such as K_n ▹ P₂, K_n ▹ P₃, Btn ▹ P₂, Bt_n ▹ P₃, and Bt_n ▹ C₃.