A Comprehensive Study of Picture Fuzzy Planar Graphs with Real-World Applications

Abstract

Picture fuzzy planar graph is a generalization of fuzzy and intuitionistic fuzzy planar graph. There are some real-life problems which cannot be handled by a fuzzy planar graph but such types of problems can efficiently be handled by a picture fuzzy planar graph. Motivated by this point of view, we consider the picture fuzzy planar graph in our research study. In this paper, we introduce picture fuzzy planar graphs, picture fuzzy dual graphs and their important properties. Also, we introduce a new concept of planarity value which satisfies the picture fuzzy criteria. An algorithm for testing the planarity of a picture fuzzy graph is also designed. Also, we provide a flowchart of the corresponding algorithm. Besides this, we propose an application for ranking the essentiality of flyover or underpass in street junctions and select the most essential street junctions where flyover or underpass is needed in a smart city.