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 A construction of commutative nilpotent semigroups Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 801-809 https://doi.org/10.4134/BKMS.2013.50.3.801Printed May 31, 2013 Qiong Liu, Tongsuo Wu, and Meng Ye Shanghai University of Electric Power, Shanghai Jiaotong University, Shanghai Jiaotong University Abstract : In this paper, we construct nilpotent semigroups $S$ such that $S^n=\{0\}$, $S^{n-1}\not=\{0\}$ and $\G(S)$ 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 $n\ge 5$. We also give counting formulae to calculate the number of the mutually non-isomorphic nilpotent semigroups when $n=5,\, 6$ and in finite cases. Keywords : nilpotent semigroup, refinement of a star graph, structure, counting formula MSC numbers : Primary 20M14; Secondary 05C90 Downloads: Full-text PDF