U.S. airline regulators have opened an investigation into Delta Air Lines, which is still struggling to restore operations on Tuesday, more than four full days after a faulty software update caused technological havoc worldwide and disrupted global air travel.Transportation Secretary Pete Buttigieg announced the Delta investigation on the X social media platform Tuesday “to ensure the airline is following the law and taking care of its passengers during continued widespread disruptions.”“All airline passengers have the right to be treated fairly, and I will make sure that right is upheld,” Buttigieg added.As of Tuesday morning, Delta had an outsized portion of canceled flights. Of the 654 total cancellations of flights within, into or out of the U.S. Delta had 440 of them, according to data posted by FlightAware as of 10:05 a.m. Eastern time. United Airlines was next among U.S. airlines with 41, followed by American with 33.Delta also had more delayed flights than any other U.S. airline, with 481, but the gap was not as wide: American had 373 flight delays.Delta did not immediately respond to a request for comment early Tuesday.In an announcement to travelers posted on its website Monday, Delta said that its crews are fully staffed, but that a critical operational system that ensures all flights have a full crew "is deeply complex and is requiring the most time and manual support to synchronize.”Buttigieg spoke to Delta CEO Ed Bastian on Sunday about the airline’s high number of cancellations. The Transportation Department said its top officials have reminded Delta of the airline’s obligation to provide refunds to passengers whose flights were canceled and who don’t want to be rebooked on a later flight.