Edberg won six Grand Slam titles and helped Sweden win four Davis Cups. Cheney, 87, has won more than 300 senior titles, including 20 senior Grand Slams. She was introduced by Hall of Famer John McEnroe.
Graf had trouble picking her favorite title. After pausing, she said her initial Wimbledon crown may have been the best.
"The good thing is there are so many to pick from," she said. "The tough thing is to pick one or a special one."
After ceremonies, Greg Rusedski earned his 14th career title at the same spot he won his first back in 1993, beating Alexander Popp, 7-6 (5), 7-6 (2), in the Hall of Fame Tennis Championships.
In other tennis news:
* Wimbledon champion Roger Federer beat Igor Andreev, 6-2, 6-3, 5-7, 6-3, to win the Swiss Open in Gstaad, Switzerland, for the first time.
* French Open champion Gaston Gaudio and Mariano Zabaleta won rain-delayed semifinals in straight sets, setting up an all-Argentine final at the Swedish Open in Bastad, Sweden. Gaudio beat Robin Soderling, 6-4, 6-2, while defending champion Zabaleta defeated Fernando Gonzalez, 6-1, 6-4.
* Medallist surged to an early lead and maintained a clear advantage the rest of the way, beating The Cliff's Edge by 3 3/4 lengths in the $150,000 Dwyer Stakes at Belmont Park.
* Favorite Star Parade cruised to a 3 1/2-length win in the $228,450 Milady Handicap at Hollywood Park in Inglewood, Calif.
* Vincent Lecavalier will replace the injured Steve Yzerman on Canada's team for the World Cup of Hockey, joining Tampa Bay teammates Brad Richards and Martin St. Louis. Team Canada named Lecavalier to the team after Yzerman, 39, told executive director Wayne Gretzky he would not be ready for the tournament, which begins Aug. 30. The Detroit captain injured his left eye during a Game 5 loss to Vancouver in the Western Conference semifinals.
* John Korir won the Boilermaker Road Race in Utica, N.Y., for the fourth time, edging fellow Kenyan Wilson Kigen-Kipkemboi on the final stride of the 15-kilometer race and finishing in 43 minutes, 50 seconds. *