We investigate some properties of Cayley fuzzy graphs on groups in terms of algebraic structures. And we also discuss the connectedness on it. In this paper, we prove that the Cayley fuzzy graph induced by (Zm × Zn, +, ν) is the disjoint union of Cay (aH, R) provided ν(h) > 0 ∀ h ∈ H and ν(h′) =0 ∀ h′∈ Zm × Zn, where H is the cyclic subgroup of order n in Zm × Zn.
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Jisha et al. (2024) studied this question.
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