“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 7380
School of Mathematics
  Title:   On commuting graphs of semisimple rings
1.  S. Akbari
2.  A. Mohammadian (Joint with M. Ghandehari and M. Hadian)
  Status:   Published
  Journal: Linear Algebra Appl.
  Vol.:  390
  Year:  2004
  Pages:   345-355
  Supported by:  IPM
Let R be a non-commutative ring. The commuting graph of R denoted by Γ(R), is a graph with vertex set R\Z(R), and two distinct vertices a and b are adjacent if ab=ba. In this paper we investigate some properties of Γ(R), whenever R is a finite semisimple ring. For any finite field F, we obtain a minimum degree, maximum degree and clique number of Γ(Mn(F)). Also it is shown that for any two finite semisimple rings R and S, if Γ(R) ≅ Γ(S),then there are commutative semisimple ring R1 and S1 and semisimple ring T such that RT×R1, ST×S1 and |R1|=|S1|.

Download TeX format
back to top
scroll left or right