Relatively prime restrained detour domination number of a graph

Consider a connected graph G=(V, E) with a minimum of two vertices. A subset ⊆ is termed a relatively prime restrained detour dominating set of G if it fulfills two conditions: firstly, S must be a relatively prime detour dominating set, and secondly, the induced subgraph should not contain any isolated vertices. The relatively prime restrained detour domination number, denoted as γrprdn(G), is defined as the minimum cardinality of such a set that satisfies these conditions. Precise values for certain standard graphs, limits and some interesting results are established.