Affiliations: [a] Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan, KPK, Pakistan
| [b] Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan
| [c] Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia
| [d] Department of Mathematics, Research Institute for Natural Sciences, Hanyang University Seoul, Republic of Korea
Correspondence:
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Corresponding author. Choonkil Park, Department of Mathematics, Research Institute for Natural Sciences, Hanyang University Seoul 04763, Republic of Korea. E-mail: baak@hanyang.ac.kr.
Abstract: The concept of the fuzzy graph (FG) and the simplification of its type have been designed with many real-world concerns, decision-making, network problems, and other types of impression in mind. This article is essentially a generalization of fuzzy graph theory with their association in settings where four organizations of membership grade are characterized by imprecision. The contemporary idea of domination in picture fuzzy graph (PFG) is given the generalization of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination is unit on the innovative idea of picture fuzzy graph. This article is the main focus on the graph of the picture fuzzy set. Additionally, this research paper concludes with the concept of domination theory (DT) and double domination theory (DDT) in the concept of environment. Obviously, the framework of picture fuzzy graph is purposed and their connected theory is obtained together with presented examples. Supplementary the domination theory (DT) in the picture fuzzy graph. A few order, strength, cardinality, and domination of completeness, neighbors in a picture fuzzy graph, and the DDS and given some examples are likewise studied in the concept of picture fuzzy graph in the environment. The application of the politician campaign is novel exploiting the projected study and curious how to double dominate would relationship with the politician campaign. Finally, a comparison between the current effort and the prior effort is made, and the advantages of the work done in the context of a picture fuzzy graph are discussed.
