A Construction of Commutative Nilpotent Semigroups

Abstract

Abstract. In this paper, we construct nilpotent semigroups S such that S n = {0}, S n−1 = {0} and Γ(S) is a refinement of the star graph K 1,n−3 with center c together with finitely many or infinitely many end vertices adjacent to c, for each finite positive integer n ≥ 5. We also give counting formulae to calculate the number of the mutually non-isomorphic nilpotent semigroups when n = 5, 6 and in finite cases.