The big chill between Rudy Giuliani and ex-wife Donna Hanover was on full display yesterday when both attended their daughter Caroline’s high school graduation – but sat as far apart as possible and never spoke.

When the commencement speaker, Sen. Charles Schumer, noted Giuliani’s presence and the audience broke into applause, Hanover and her son, Andrew Giuliani, sat stone-faced and didn’t clap.

But Hanover and Andrew jumped up and cheered when the Harvard-bound 17-year-old Caroline received her diploma from the tony Trinity School, while Giuliani and his wife, Judith, didn’t even crack a smile.

During the two-hour graduation, the Giulianis could be seen whispering to each other and peering over at a happy Hanover and her husband, Edwin Oster, sitting 30 yards away.

Rudy and Judith Giuliani avoided his children and ex-wife by arriving minutes before the ceremony began, entering through a side entrance, and they ducked out 10 minutes before it ended.

Hanover, Andrew and a group of family friends arrived at least an hour early to secure the best seats at the Crenshaw Church on West 96th Street and Central Park West.

The Republican presidential front-runner’s strained relationship with his children burst into public view earlier this year

after Andrew told a reporter that he was estranged from his father and had a “problem” with his stepmom, Judith.

The former mayor did not attend Andrew’s high school graduation and has reportedly missed many of Caroline’s high school performances.

At the graduation yesterday, Andrew did not acknowledge his father and stepmother and would not say whether the couple would join them later.

“We plan to celebrate privately with friends and family. We’re all so proud of her and it’s really Caroline’s day,” said Andrew, wearing a Yankees tie.

When reporters asked Hanover whether she would celebrate with Giuliani, she grimaced, then gushed at how happy she was for her daughter.

The Giulianis also wouldnot comment.

elizabeth.wolff@nypost.com