Abstract
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.
Highlights
A graph is an easy way to express information, together with the relationship between various kinds of entities
The purpose to propose these perceptions to fuzzy incidence graphs (FIGs) is that Selvam and Ponnappan [38] proposed the idea of domination in the join of Fuzzy graphs (FGs) using strong edges (SEs), and Ponnappan and Selvam [39]
Different authors have investigated more than thirty domination parameters
Summary
A graph is an easy way to express information, together with the relationship between various kinds of entities. We are unable to apply FGs to the real-life application provided in Section 6 of SPDN in matters of trade of different countries because FGs do not have a feature to give the impact of a vertex on an edge but FIGs have this property. This deficiency of FGs motivates us to introduce these ideas for FIGs. Secondly, the purpose to propose these perceptions to FIGs is that Selvam and Ponnappan [38] proposed the idea of domination in the join of FGs using strong edges (SEs), and Ponnappan and Selvam [39].
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