Competition graphs under complex Pythagorean fuzzy information

A complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is useful model to deal the vagueness with the degrees whose ranges are extended from real to complex subset with unit circle. This set deals with vagueness and periodicity more precisely as compared to complex fuzzy set and complex intuitionistic fuzzy set. In this paper, we propose a new graph, complex Pythagorean fuzzy competition graph by combining the complex Pythagorean fuzzy information with competition graph. We also investigate the two extensions of complex Pythagorean fuzzy competition graphs, namely, complex Pythagorean fuzzy k -competition and complex Pythagorean fuzzy p -competition graphs. Moreover, we present complex Pythagorean fuzzy neighborhood graphs and m -step complex Pythagorean fuzzy competition graphs. In addition, we illustrate an application of complex Pythagorean fuzzy competition graphs with algorithm to highlight the importance of these graphs in real life.

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