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Article

Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries

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Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
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Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203 Cartagena, Spain
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Nonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
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Author to whom correspondence should be addressed.
Academic Editors: Jian-Qiang Wang and László T. Kóczy
Symmetry 2021, 13(7), 1279; https://doi.org/10.3390/sym13071279
Received: 1 June 2021 / Revised: 8 July 2021 / Accepted: 12 July 2021 / Published: 16 July 2021
Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), are an applicable and well-organized tool to epitomize and resolve multiple real-world problems in which ambiguous data and information are essential. In this article, we extend the idea of domination of FGs to the FIG using strong pairs. An idea of strong pair dominating set and a strong pair domination number (SPDN) is explained with various examples. A theorem to compute SPDN for a complete fuzzy incidence graph (CFIG) is also provided. It is also proved that in any fuzzy incidence cycle (FIC) with l vertices the minimum number of elements in a strong pair dominating set are M[γs(Cl(σ,ϕ,η))]=l3. We define the joining of two FIGs and present a way to compute SPDN in the join of FIGs. A theorem to calculate SPDN in the joining of two strong fuzzy incidence graphs is also provided. An innovative idea of accurate domination of FIGs is also proposed. Some instrumental and useful results of accurate domination for FIC are also obtained. In the end, a real-life application of SPDN to find which country/countries has/have the best trade policies among different countries is examined. Our proposed method is symmetrical to the optimization. View Full-Text
Keywords: strong pair domination; accurate domination; fuzzy incidence graph; complete fuzzy incidence graph strong pair domination; accurate domination; fuzzy incidence graph; complete fuzzy incidence graph
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MDPI and ACS Style

Nazeer, I.; Rashid, T.; Hussain, M.T.; Guirao, J.L.G. Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries. Symmetry 2021, 13, 1279. https://doi.org/10.3390/sym13071279

AMA Style

Nazeer I, Rashid T, Hussain MT, Guirao JLG. Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries. Symmetry. 2021; 13(7):1279. https://doi.org/10.3390/sym13071279

Chicago/Turabian Style

Nazeer, Irfan, Tabasam Rashid, Muhammad T. Hussain, and Juan L.G. Guirao 2021. "Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries" Symmetry 13, no. 7: 1279. https://doi.org/10.3390/sym13071279

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