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

Bhat, V. K.; Raina, Ravi; Nehra, Neeraj; Prakash, Om

Int. J. Contemp. Math. Sci. 2, No. 13-16, 667-671 (2007).

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

Keywords:

zero-divisors; non-commutative rings; directed graphs; planar graphs