Abstract
Let S be a semigroup. This paper studies the intersection graphs of fuzzy semigroups. It is shown that the fuzzy intersection graph Int(G(S)), of S, is complete if and only if S is power joined. If Γ(S) denotes the set of all fuzzy right ideals of S, then the fuzzy intersection graph Int(Γ(S)) is complete if and only if S is fuzzy right uniform. Moreover, it is shown that Int(Γ(S)) is chordal if and only if for a,b,c,d ∈ S, some pair from {a,b,c,d} has a right common multiple property. It is also shown that if Int(G(S)) is complete and S has the acc on subsemigroups, then S is cyclic.
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