Neighbourhood and competition graphs under fuzzy incidence graph and its application

Competition graphs, which are mathematical representations of competitive relationships among entities, have found applications in various domains. This article introduces and explores several types of graphs, including fuzzy incidence competition graphs, fuzzy incidence neighborhood graphs, p-competition fuzzy incidence graphs, m-step fuzzy incidence competition graphs, and m-step fuzzy incidence neighborhood graphs. We establish sufficient conditions under which an edge is independent strong or independent incidence strong. Relation between competition graphs of isomorphic fuzzy incidence digraphs is established. Through rigorous analysis, several intriguing results concerning these graphs are derived. Additionally, at the end of the article, we evaluate a group of researchers using fuzzy incidence graphs to identify the most influential member within the group.