The Chromatic Number of Zero-divisor Graphs (I)

Qiong LIU

Department of Mathematics, Shanghai University of Electric Power, Shanghai, 200090, CHINA

Abstract: In this paper, we discuss the chromatic number of the zero-divisor graphs (R) . We study the algebraic

structure and properties of commutative rings whose zero-divisor graphs have its chromatic number

equals one ｏｒ two. Furthermore, we completely determine the algebraic structure of rings R.

Keywords: Commutative rings; Star graphs; Two-star graphs; Bipartite graphs.