The zero divisor graph of 2 x 2 matrices over a field

Abstract

A zero divisor graph, Γ(R), is formed from a ring R by having each element of Z(R)\{0} to be a vertex in the graph and having two vertices u and v adjacent if the corresponding elements from the ring are nonequal and have product equal to zero. In this paper, the structure of the zero-divisor graph of 2 x 2 matrices over a field, Γ(M₂(F)), are completely determined.

Mathematics Subject Classification (2010): Primary 13A99; Secondary 16U99, 05C50.

Keywords: Zero divisor graph, ring, A-join of graphs