Abstract
In this chapter, we discuss the concept of bipolar fuzzy competition graphs and present several notions concerning bipolar fuzzy out neighborhoods, bipolar fuzzy in neighborhoods, bipolar fuzzy open neighborhood graphs, bipolar fuzzy closed neighborhood graphs, bipolar fuzzy \(\textit{\textbf{k}}-\)competition graphs, and underlying bipolar fuzzy graphs. We describe various methods for the construction of bipolar fuzzy competition graphs of certain products of bipolar fuzzy digraphs. Using various constraints, we study the relations of bipolar fuzzy \([\textit{\textbf{k}}]-\)competition graphs, bipolar fuzzy \((\textit{\textbf{k}})-\)competition graphs, and underlying bipolar fuzzy graphs. We elaborate certain algorithms to compute the strength of competition with a number of real-world applications in different fields including food webs, business marketing, politics, wireless communication networks, and social networking.
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