  The signless Laplacian Q and signless edge-Laplacian S of a given graph may
or may not be invertible. The Moore-Penrose inverses of Q and S are studied. In
particular, using the incidence matrix, we find combinatorial formulas of the
Moore- Penrose inverses of Q and S for trees. Also we present combinatorial
formulas of the inverses of Q and S for odd unicyclic graphs.
