Commuting graphs of full matrix rings over finite fields Original Research Article

Let R be a non-commutative ring and Z(R) be its center. The commuting graph of R is defined to be the graph Γ(R) whose vertex set is R-45 degree ruleZ(R) and two distinct vertices are joint by an edge whenever they commute. Let F be a finite field, ngreater-or-equal, slanted2 an arbitrary integer and R be a ring with identity such that Γ(R)congruent withΓ(Mn(F)), where Mn(F) is the ring of n×n matrices over F. Here we prove that R=Mn(F). We also show that if F is prime and n=2, then Rcongruent withM2(F).