演講者：江謝宏任教授
單 位：國立中正大學數學系
日 期：2009年9月22日 PM 14:30
地 點：國立高雄大學理學院408室
講 題：Embedding of the Zero-divisor Graph and its Associated Line Graph
摘 要：
Let R be a commutative ring with identity. The zero-divisor graph of R, denoted by \Gamma(R), is an undirected simple graph associated to the ring R such that its vertex set consists of all nonzero zero-divisors of R and that two distinct vertices are joined by an edge whenever the product of the vertices is zero. The interplay between the ring-theoretical properties and the graph-theoretical properties of the zero-divisor graph is the core of our study. In this talk, the basic properties of the zero-divisor graphs and their line graphs will be discussed. Moreover, I will introduce the genus formula for minimal embeddings of some special graphs into compact surfaces and apply them to the embedding problems related to zero-divisor graphs. A complete classification of rings with toroidal and projective zero-divisor graphs will be given through the talk.
