Michael Graham, whose admission and eligibilty were in doubt after he signed a national letter of intent, has been admitted to Georgetown University and will be eligible to play this season, Coach John Thompson said yesterday.

In a separate and unrelated development, two-year letterman Anthony Jones, from Dunbar High, said he will transfer to Nevada-Las Vegas. Jones had said last month he would not play for the Hoyas this season because of personal reasons, but that he would return for the 1984-85 season.

Graham, a 6-foot-9 forward from Spingarn High School, may be the strong rebounding forward Georgetown has needed. Thompson said Graham was admitted to the university Friday and will be on full athletic scholarship.

The NCAA had said previously that Graham would not be eligible to play this year, having based its decision on the assumption that Graham completed high school in eight semesters.

But Graham went to high school 7 1/2 semesters, and reached the required 2.0 grade average and received his high school diploma by passing courses in math and English this summer in the Upward Bound program at Georgetown. The program is accredited by the D.C. public school system.

Graham will enroll at Georgetown Monday, Thompson said.

Dave Berst of the NCAA said Graham apparently has fulfilled all obligations in order to be eligible this season.

It has been a stormy year for Graham, who said it bothered him to hear questions about his character and discipline. He was also caught in the middle of a feud between his high school coach, John Wood, and at least one of the school's teachers.

"It feels great just being able to start all over again," Graham said yesterday. "When I read the things people were saying about me, I thought it was another guy named Michael Graham . . . At one point, I never thought I'd get to college. My high school coach told me it would be impossible unless I got a GED (General Equivalency Diploma) and went to a junior college.

"Then, I got to talk to Coach Thompson, and he told me to listen to him, and I wouldn't be sorry," Graham said. "This is a chance to straighten out my life. In the past, I just didn't want to attend school, so people thought I was a problem child.

"I was a problem--but only to myself; now I look to have a future. Mr. Thompson talked straight to me. He told me I had to get squared away . . .

"I think the Upward Bound program prepared me for college. People were pretty friendly, but they asked a lot of questions; like, would I predict (achieve a 2.0 high school average), and if I was going to play basketball this year. I thought about guys in my neighborhood, who stand around and talk about what they used to be. I don't want to be out on a corner five years from now telling some kid about what I could have been."

Thompson said yesterday his biggest concern when he first talked to Graham was whether the player, who is 20, would work and make the necessary commitment.

"I made it very clear to him that I'm not going to put up with anybody who's not going to work to get an education," Thompson said yesterday. "He's had a very unstable life. But beyond a doubt, to me, he's shown every intention he will move toward a degree.

"I asked a number of people, 'What kind of kid is this?' And 99 percent of the people I talked to--teachers of his, people he worked with, et cetera--liked him as a person," Thompson said. "Red Jenkins (coach at W.T. Woodson) approached me and said he had dealt with Michael and found him very responsive to discipline. The most important thing for me was to know him, and not deal with his reputation."

Thompson was in Las Vegas, preparing to visit with officials from UNLV to talk about Jones, a regular the past two seasons and a big part of Georgetown's 1982 NCAA tournament runner-up.

Yesterday, Jones said, "I had to take some time off to get some things straight at home. I thought about coming back, but I would still have the same problems. I wanted to expand a little bit and get away from home. I think by going away, I can really concentrate and things will be more meaningful. Basically, I decided to transfer because I wanted to, not because someone told me to."