Domination in Inverse Fuzzy Mixed Graphs with Application
Rahul Mondal
1
(
Department of Mathematics, Vivekananda Satavarshiki Mahavidyalaya, Manikpara, Jhargram -721513, West Bengal, India.
)
Ganesh Ghorai
2
(
Department of Applied Mathematics, Vidyasagar University, Midnapore - 721 102, West Bengal, India.
)
الکلمات المفتاحية: Inverse fuzzy mixed dominating function, Inverse fuzzy mixed domination number, Upper inverse fuzzy mixed domination number, (g, h)- inverse fuzzy mixed dominating set.,
ملخص المقالة :
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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