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

2007/01/23 by Maimani, Hamid Reza, Mogharrab, Mojgan, Yassemi, Siamak
#13A99 #20M14 #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0701627

Abstract

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.

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