On resolving perfect dominating number of comb product of special graphs
M O Aziza, Dafik Dafik, Arika Indah Kristiana, Ridho Alfarisi, Dwi Agustin Retnowardani · Journal of Physics Conference Series · 2021
Abstract 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 = {w 1,w 2,…,wk } ⊆ 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 Wrp Ç V (G) is called the resolving perfect dominating set on graph G if Wrp 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 γrpG. In this study, we analyzed the resolving perfect dominating number of comb product operations between two connected graphs, such as Kn ▹ P 2, Kn ▹ P 3, Btn ▹ P 2, Btn ▹ P 3, and Btn ▹ C 3.