Abstract
The notion of competition graphs has a wide range of applications and has been utilized in designing various ecological problems and real-world competitions. Here, the idea of m-step inverse fuzzy mixed competition graphs has been introduced and some of its basic properties have been discussed. Also, some ideas associated with the concept of m-step inverse fuzzy mixed competition graphs, such as m-step inverse fuzzy neighborhood graph, inverse fuzzy mixed economic competition graph, and m-step inverse fuzzy mixed economic competition graph have been defined. Our motive was to focus on the real-life problems that can be properly addressed with graphs involving directed and undirected edges. In this case, the concept of an m-step fuzzy competition graph is not appropriate for solving these problems. However, the idea of m-step inverse fuzzy mixed competition graphs is more relevant to address them. An application of m-step inverse fuzzy mixed competition graphs has been identified as a suitable solution to a real-life problem.
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