On C-commuting graph of matrix algebra

Abstract

Let D be a division ring, n 2 a natural number, and C ⊆ M_n(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 M_n(D)is defined and denoted by ΓC(Mn(D)). Conditions are given that guarantee that the C−commuting graph is connected.