Dominations in Intutionistic Fuzzy Directed Graphs with Applications towards Influential Graphs

Hao Guan, Waheed Ahmad Khan (), Amna Fida, Khadija Ali, Jana Shafi and Aysha Khan
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Hao Guan: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Waheed Ahmad Khan: Division of Science and Technology, Department of Mathematics, University of Education Lahore, Attock Campus, Attock 43600, Pakistan
Amna Fida: Division of Science and Technology, Department of Mathematics, University of Education Lahore, Attock Campus, Attock 43600, Pakistan
Khadija Ali: Division of Science and Technology, Department of Mathematics, University of Education Lahore, Attock Campus, Attock 43600, Pakistan
Jana Shafi: Department of Computer Engineering and Information, College of Engineering in Wadi Alddawasir, Prince Sattam Bin Abdulaziz University, Wadi Alddawasir 11991, Saudi Arabia
Aysha Khan: Department of Mathematics, Prince Sattam Bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia

Mathematics, 2024, vol. 12, issue 6, 1-14

Abstract: In this manuscript, we introduce a few new types of dominations in intuitionistic fuzzy directed graphs (IFDGs) based on different types of strong arcs (SAs). Our work is not only a direct extension of domination in directed fuzzy graphs (DFGs) but also fills the gap that exists in the literature regarding the dominations in different extended forms of fuzzy graphs (FGs). In the beginning, we introduce several types of strong arcs in IFDGs, like semi- β strong arcs, semi- δ strong arcs, etc. Then, we introduce the concepts of domination in IFDGs based on these strong arcs and discuss its various useful characteristics. Moreover, the dominating set (DS), minimal dominating set (MDS), etc., are described with some fascinating results. We also introduce the concept of an independent set in IFDGs and investigate its relations with the DS, minimal independent set (MIS) and MDS. We also provide numerous important characterizations of domination in IFDGs based on minimal and maximal dominating sets. In this context, we discuss the lower and upper dominations of some IFDGs. In addition, we introduce the terms status and structurally equivalent and examine a few relationships with the dominations in IFDGs. Finally, we investigate the most expert (influential) person in the organization by utilizing the concepts of domination in IFGs.

Keywords: IFDGs; strong arcs; domination in IFDG; independent set; minimal and maximal dominating sets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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