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Let C be a set of all structures (Sf , A) where S is a semigroup, f is an endomorphism on S and A is a subset of S. We define operation ⊗ on C and also prove (C,⊗) is a semigroup. Similarly, we show D, the set of all endo-Caylay sigraphs, is a semigroup under the tensor product. Moreover, we find partial order relations in both C and D.

THE PARTIAL ORDER ON CATEGORY OF SEMIGROUPS AND ENDO-CAYLEY DIGRAPHS