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

Maimani, Hamid Reza; Mogharrab, Mojgan; Yassemi, Siamak

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

Authors

Maimani, Hamid Reza

Mogharrab, Mojgan

Yassemi, Siamak

Description

For a commutative semigroup $S$ with 0, the zero-divisor graph of $S$ denoted by $Γ(S)$ is the graph whose vertices are nonzero zero-divisor of $S$, and two vertices $x$, $y$ are adjacent in case $xy=0$ in $S$. In this paper we study the case where the graph $Γ(S)$ is complete $r$-partite for a positive integer $r$. Also we study the commutative semigroups which are finitely colorable.
11 pages