Zero-divisor Semigroups of Star Graphs and Two-star Graphs

Gaohua Tang1, Huadong Su1, Beishang Ren1
1School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, Guangxi, 530001, P. R. China

Abstract

The zero-divisor graph of a commutative semigroup with zero is a graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices joined by an edge if their product in the semigroup is zero. In this paper, we provide formulas to calculate the numbers of non-isomorphic zero-divisor semigroups corresponding to star graphs \(K_{1,m}\), two-star graphs \(T_{m,n}\), and windmill graphs, respectively.