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A CONSTRUCTION OF COMMUTATIVE NILPOTENT SEMIGROUPS
Liu, Qiong,Wu, Tongsuo,Ye, Meng Korean Mathematical Society 2013 대한수학회보 Vol.50 No.3
In this paper, we construct nilpotent semigroups S such that $S^n=\{0\}$, $S^{n-1}{\neq}\{0\}$ and ${\Gamma}(S)$ 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 $n{\geq}5$. We also give counting formulae to calculate the number of the mutually non-isomorphic nilpotent semigroups when $n=5$, 6 and in finite cases.
A construction of commutative nilpotent semigroups
Qiong Liu,Tongsuo Wu,Meng Ye 대한수학회 2013 대한수학회보 Vol.50 No.3
In this paper, we construct nilpotent semigroups S such that Sn = {0}, Sn−1 6≠{0} and Γ(S) is a refinement of the star graph K1,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 nilpo- tent semigroups when n = 5, 6 and in finite cases.