[12] When he returned, he worked as a teacher and basketball coach at Georgetown High School before pursuing his master's degree in education administration at the University of Kentucky.
[5] After graduating in 1958, he returned to Georgetown and stayed for an additional seven years, where he was a teacher, basketball coach, and at one point even held the role of acting principal.
[15] He then worked for the State Highway Department in Frankfort as an administrative assistant from 1969 to 1971[5] and briefly coached basketball at Danville Bate Junior High in 1971.
[20] He was elected Mayor of Frankfort in 2008, succeeding Bill May, who did not seek re-election due to state law prohibiting campaigning for a fourth consecutive term.
[23][2] Graham and Carol Miller, who he met while studying at Cumberland College, were engaged in August 1951 and had three children: Lynn, Randy, and Ray.
[5][27] Following their divorce, Graham entered a committed relationship with Karen Schmalzbauer, who has worked extensively in Kentucky's Department of Education.
[28][29][6] Schmalzbauer is one of the founders of Hope Harbor, a non-profit counseling center that supports survivors of sexual assault and their families.