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

  • Ali Reza Ashrafi
  • Adel Tadayyonfar
Keywords: Zero divisor graph, ring, A-join of graphs

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 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

Published
2016-11-25
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606