On resolving perfect dominating number of comb product of special graphs

A set of vertices D subset of 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 v is an element of V(G), the k-vector r(v\W) is called the metric code or location W, where W = {w(1), w(2), ..., w(k)} subset of V (G). An ordered set W subset of V (G) is called the resolving set of graph G if each vertex u, v is an element of V (G) has a different point representation with respect to the W where r(u\W) not equal r(v\W). The ordered set W-rp subset of 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 (gamma rp)G. In this study, we analyzed the resolving perfect dominating number of comb product operations between two connected graphs, such as K-n (sic) P-2, K-n (sic) P-3, Bt(n) (sic) P-2, Bt(n) (sic) P-3, and Bt(n) (sic) C-3.