Her contribution to golf was her administrative and officiating capabilities more than her individual golfing skill.
She was chairman of the United States Golf Association (USGA) Women's Committee 1987 and 1988, the highest volunteer position in women's golf.
The committee conducts or supervises golf tournaments for women, mostly amateur events (except for the U.S.
Open) and selects the Curtis Cup members.
In this role, Graham was responsible for running the USGA's top three women's events: the Open, the Amateur, and the Mid-Amateur.
In each of these championships Graham, an expert on the rules of golf, accompanied the final group on the day of the final round.
She has selected and handicapped golf courses for women's competitions and has officiated at international golf competitions in Europe, South America and China.
She was appointed by the USGA as (non-playing) captain of the 1990 United States World Amateur golf team which won the international competition that year in New Zealand.
From 1973 to 1975 she was president of the Women's Southern Golf Association (WSGA).
The organization later established a perpetual trophy in her honor named the "Katherine Graham Senior Championship Trophy".
Tennessean sportswriter Jimmy Davy called Graham "one of the most influential people in women's amateur golf".