Fuzzy k-Competition Graphs and p-Competition Fuzzy Graphs

Fuzzy competition graph as a generalization of competition graph is introduced here. Two generalizations of fuzzy competition graph as fuzzy k-competition graphs and p-competition fuzzy graphs are also defined. These graphs are related to fuzzy digraphs. Fuzzy neighbourhood graphs, related to fuzzy graphs, are also defined here. Besides, some relations between fuzzy competition graphs and fuzzy neighbourhood graphs have been established. And finally, several results to find strong edges of the above mentioned graphs have also been established.