Domination in Inverse Fuzzy Mixed Graphs with Application

Rahul Mondal ¹ ( )
Ganesh Ghorai ² ( )

Submited date : 2025-06-07 Accepted date : 2025-08-24

Keywords: Inverse fuzzy mixed dominating function, Inverse fuzzy mixed domination number, Upper inverse fuzzy mixed domination number, (g, h)- inverse fuzzy mixed dominating set.,

Abstract :

In the first part of our work‎, ‎the concepts of inverse fuzzy mixed dominating set (IFMDS) and inverse fuzzy mixed domination number (IFMDN) have been explored for inverse fuzzy mixed graphs (IFMGs)‎. ‎Based on these ideas‎, ‎the inequality $\mathcal{R}^{ir} \leq \mathcal{R}^{\gamma} \leq \mathcal{R}^{i} \leq \mathcal{R}^{\beta_{0}} \leq \mathcal{R}^{\Gamma} \leq \mathcal{R}^{IR}$ has been established for an IFMG $\mathcal{R}$‎. ‎In the second part of our work‎, ‎we have explored the concept of $(g‎, ‎h)$-IFMDS‎, ‎which is defined as a fuzzy subset of the membership function of nodes‎. ‎Most importantly‎, ‎the relation $ (g,h)$-IN$(\mathcal{R}$) $\leq (g,h)$-DN$(\mathcal{R}$)$\leq (g,h)$-UDN$(\mathcal{R}$)$\leq (g,h)$-UIN$(\mathcal{R})$ has been established for an IFMG $\mathcal{R}$‎. ‎At the end‎, ‎a real-life application of the concept of $(g‎, ‎h)$-IFMDS is given‎.

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