## A note on zero divisor graph over rings.(English)Zbl 1138.16304

Summary: We discuss the graphs of the sets of zero-divisors of a ring. Now let $$R$$ be a ring. Let $$G$$ be a graph with elements of $$R$$ as vertices such that two non-zero elements $$a,b\in R$$ are adjacent if $$ab=ba=0$$. We examine such a graph and try to find out when such a graph is planar and when is it complete etc.

### MSC:

 16U99 Conditions on elements 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C20 Directed graphs (digraphs), tournaments
Full Text: