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Paper   IPM / M / 11317
School of Mathematics
  Title:   On commuting graphs of finite matrix rings
  Author(s):  A. Mohammadian
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  38
  Year:  2010
  Pages:   988-994
  Supported by:  IPM
The commuting graph of a ring R, denoted by \mathnormalΓ(R), is a graph whose vertices are all noncentral elements of R and two distinct vertices are joint by an edge whenever they commute. It is conjectured that if R is a ring with identity such that \mathnormalΓ(R) ≅ \mathnormalΓ(Mn(F)), for a finite field F and n ≥ 2, then RMn(F). Here we prove this conjecture when n=2.

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