Abstract
Presently, fuzzy graph theory has wide applications in engineering and social networks. Based on the applications, different types of fuzzy graphs are defined. Among them the competition graph is significantly used to model ecological problems. This graph is one kind of intersection graph. Different competitions of real world have been designed by fuzzy competition graphs. One generalization of fuzzy competition graph, called $$m$$ -step fuzzy competition graph, is defined in this paper. Some related fuzzy graphs including fuzzy $$m$$ -step neighbourhood graph, fuzzy economic competition graphs and fuzzy $$m$$ -step economic competition graphs are introduced. Some properties of these new graphs have been investigated.
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