Abstract
The q-rung orthopair fuzzy graph (q-ROFG) is an expansion of the intuitionistic fuzzy graph (IFG) and Pythagorean fuzzy graph (PFG); q-rung orthopair fuzzy model is an influential model for describing vagueness and uncertainty as a comparison to an intuitionistic fuzzy model and Pythagorean fuzzy model. The research aims to illustrate the notion of the graph of q-rung orthopair fuzzy sets (q-ROFSs). Furthermore, in this article, we examine the ideas of domination theory (DT) and double domination theory (DDT) in q-ROFGs. Additionally, the structure of q-ROFG is developed and its associated concept is presented through the assistance of instructive instances. Furthermore, the DT of q-ROFGs is established, as are cardinality, power, and completeness on dominance in a q-ROFG and bipartite q-ROFG, and double domination set (DDS), as well as some results, is investigated in the concept of q-ROFGs. A political campaign is simulated using the proposed structure as an application, and the impact of double dominance (DD) on political campaigns is investigated. Finally, a comparison is given between the proposed study and actual studies, as well as the advantages of working in the q-ROFG scenario.