Let (Formula presented.) be the set of (Formula presented.) matrices over a division ring (Formula presented.). Two matrices (Formula presented.) are adjacent if (Formula presented.). By the adjacency, (Formula presented.) is a connected graph. Suppose (Formula presented.) are division rings and (Formula presented.) are integers. When (Formula presented.), we characterize the graph homomorphism (Formula presented.) if (Formula presented.) and there exists (Formula presented.) such that (Formula presented.). © 2018, ©...