Bicycling Is The State Sport of Delaware. Delaware Accepted Bicycling as the official State sport in 2014. Cycling, also called or bicycling, is the use of bicycles for transport, recreation or sport. The Brilliant Tiger Swallowtail Butterfly was designated the official State Butterfly of Delaware June 10, 1999. The Scientific Name of Tiger Swallowtail Butterfly Is “Pterourus glaucus”.