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

Hamid Reza Maimani; Mojgan Mogharrab; Siamak Yassemi

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

Group Theory 2007-05-23 v1 Commutative Algebra

Authors: Hamid Reza Maimani , Mojgan Mogharrab , Siamak Yassemi

Abstract

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 adjacent in case $xy=0$ in $S$ . In this paper we study the case where the graph $\Gamma(S)$ is complete $r$ -partite for a positive integer $r$ . Also we study the commutative semigroups which are finitely colorable.

Keywords

zero-divisor graphs graph theory of groups graph coloring

Cite

@article{arxiv.math/0701627,
  title  = {Complete $r$-partite zero-divisor graphs and coloring of commutative semigroups},
  author = {Hamid Reza Maimani and Mojgan Mogharrab and Siamak Yassemi},
  journal= {arXiv preprint arXiv:math/0701627},
  year   = {2007}
}

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11 pages

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

Abstract

Keywords

Cite

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