Fig. 8 | Scientific Reports

Fig. 8

From: Bipolar fuzzy outerplanar graphs approach in image shrinking

Fig. 8

(a) Connected bipolar fuzzy outerplanar graph \(\psi\). (b) Bipolar fuzzy dual graph has bipolar fuzzy outerplanar graph \({\psi }^{*}\). (c) Vertex deletion bipolar fuzzy outerplanar graph \({\psi }^{*}-v\). (a)–(c) Example for bipolar fuzzy outerplanar graph \(\psi\) has bipolar fuzzy dual graph \({\psi }^{*}\) then there exist \(\mathfrak{v}\) such that \({\psi }^{*}-\mathfrak{v}\) contains no bipolar fuzzy cycle.

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