Table 4 Calculation of order and size of these vertex deletion bipolar fuzzy outerplanar subgraphs.
From: Bipolar fuzzy outerplanar graphs approach in image shrinking
S. no | Subset | Vertex deleted bipolar fuzzy outerplanar subgraph | Positive membership \({\mu }_{\mathring{\rm A}}^{\mathcal{P}}\left(\mathcalligra{x}\right)\) order | Negative membership \({\mu }_{\mathring{\rm A}}^{\mathcal{N}}(\mathcalligra{x})\) order | Positive membership \({\mu }_{\mathcal{B}}^{\mathcal{P}}(\mathcalligra{y})\) size | Negative membership \({\mu }_{\mathcal{B}}^{\mathcal{N}}(\mathcalligra{y})\) size |
|---|---|---|---|---|---|---|
1 | \({\mathbb{W}}_{1}={\mathfrak{v}}_{1}\)(0.25, − 0.3) | \(\psi -{\mathbb{W}}_{1}\) | 2.05 | 2.6 | 0.85 | 1.15 |
2 | \({\mathbb{W}}_{2}={\mathfrak{v}}_{2}\)(0.35, − 0.7) | \(\psi -{\mathbb{W}}_{2}\) | 1.95 | 2.2 | 1.2 | 1.5 |
3 | \({\mathbb{W}}_{3}={\mathfrak{v}}_{3}\)(0.4, − 0.5) | \(\psi -{\mathbb{W}}_{3}\) | 1.9 | 2.4 | 0.9 | 1.1 |
4 | \({\mathbb{W}}_{4}={\mathfrak{v}}_{4}\)(0.7, − 0.8) | \(\psi -{\mathbb{W}}_{4}\) | 1.6 | 2.1 | 1.4 | 1.9 |
5 | \({\mathbb{W}}_{5}={\mathfrak{v}}_{5}(\) 0.15, − 0.1) | \(\psi -{\mathbb{W}}_{5}\) | 2.15 | 2.8 | 1.65 | 1.95 |
6 | \({\mathbb{W}}_{6}={\mathfrak{v}}_{6}\)(0.45, − 0.5) | \(\psi -{\mathbb{W}}_{6}\) | 1.85 | 2.4 | 1.3 | 1.9 |
