She ran for the office of Attorney General in
1992, while she was pregnant with her first child. She had her baby two days after the State Democratic Convention. In the general election, she defeated Iron County Attorney Scott Burns, getting 49% of the statewide vote. She was re-elected in
1996 in a rematch with Burns with 52% of the vote. Graham made the state of Utah a plaintiff in landmark tobacco legislation. The litigation included arguments over the Attorney General's power, both from the tobacco companies, and from Utah's Governor,
Michael Leavitt. The struggle between Utah's only Democratic statewide officeholder and the state's Republican legislature and Governor resulted in passage of a law requiring the Governor's approval on any civil litigation. The Attorney General sued, a compromise was reached, and the law was ultimately repealed. At the end of her second term, Graham was one of two women on the
Deseret News list of Utah's most powerful people. ==Later life and death==