Complete $r$-partite zero-divisor graphs and coloring of commutative semigroups

Hamid Reza Maimani, Mojgan Mogharrab, Siamak Yassemi

For a commutative semigroup $S$ with 0, the zero-divisor graph of $S$ denoted by $\Gamma (S)$ is the graph whose vertices are nonzero zero-divisor of $S$, and two vertices $x$, $y$ are a…