A　generalized　polyomino　graph　is　regular　if　it　can　be　subjected　to　a　series　of　special　cell-shedding　transformations,　square　by　square,　down　to　a　single　square.　In　this　paper,　we　give　a　necessary　and　sufficient　condition　to　determine　whether　or　not　a　generalized　polyomino　graph　is　regular.　©　2006　Springer　Science+Business　Media,　Inc.