Abstract
In this chapter, we study the concepts of bipolar fuzzy multisets, bipolar fuzzy multigraphs, strong and complete bipolar fuzzy multigraphs, bipolar fuzzy planar graphs, and bipolar fuzzy dual graphs. We discuss different types of bipolar fuzzy edges, intersection value and planarity value of bipolar fuzzy graphs, strong and weak bipolar fuzzy faces, and the relation of planarity and duality in bipolar fuzzy graphs. We elaborate various properties of bipolar fuzzy bridges, bipolar fuzzy cut vertices, bipolar fuzzy blocks, bipolar fuzzy cycles, and bipolar fuzzy trees in terms of level graphs. We describe the importance of bipolar fuzzy planar graphs with a number of real-world applications in road networks and electrical connections. The main results of this chapter are from [6, 7].
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