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Let D be a division ring, n 2 a natural number, and C ⊆ Mn(D). Two matrices A and B are called C−commuting if there is C ∈ C that AB −BA = C. In this paper the C−commuting graph of Mn(D) is defined and denoted by Γ C (Mn(D) ). Conditions are given that guarantee that the C−commuting graph is connected.doi:10.13001/1081-3810.1319 fatcat:b77533ok3rfwfhsdgao3w5vx2e