Linear operators that strongly preserve graphical properties of matrices — II Original Research Article

An operator on the set M of n × n matrices strongly preserves a subset F if it maps F into F and M\F into M\F. We partition the family of n × n (0, 1)-matrices with zero diagonal into sixteen subfamilies. By examining the corresponding digraphs, we characterize the semigroups of the linear operators strongly preserving twelve of these families. We find that all of the strong preservers are nonsingular. For eight of the twelve families, the strong preservers are generated by transposition, permutational similarity and positive scaling.