After college, Graham became a teacher and band director. This led to the position of high school administrator. He later started as a sanitarian in public health. This job was described by Vic Ehlers as an educator trained in Environmental Science. Graham joined the newly formed Central Texas Health Department housed in Belton in this capacity. He was the sanitarian for Williamson County and he stressed community involvement in educating and improving the health of Central Texas Citizens by developing surveys of Family Health for the school/public health nurse to give in the schools. Graham and Herbert Hardy did a home and business survey of Fort Hood.

Graham came to the Texas Department of Health in 1932 when it was housed in the Old Land Office Building near the capitol. He worked with developing techniques for sanitarians to code daily activities and conducted food handling schools. With others he developed a test book for this course and an 8 mm film: "Hash Slinging to Food Handlers". Movies were novel at this time and the film was used through out the United States. Graham encouraged community involvement in making films. Graham and Karl Maning made other public health films and spot announcements for the state and local health departments.

Graham left the Health Department to make films. He later returned with the Aides Egypti mosquito program under Ken Lauderdale and in the Tuberculosis program under Albert Randall, MD. He retired from TDH in 1960 and joined the American Lung Association (ALA) in Dallas. After retiring from ALA he developed and presented workshops on work site wellness and health and safety.

Graham Smoot was president of the Texas Public Health Association in 1952. He was active and supportive of the Texas Environmental Health Association and the Texas Society for Public Health Education until his death in September of 1998. His vision of the public health museum came into existence in 1992 and became a separate entity from TPHA in 1996, chartered in Texas as a non-profit corporation with its own 501(C) (3) status.The Museum lives on to recognize the past in Public Health and to encourage cooperation to reach the future goals of Public Health in our State and Nation.

Graham was married to Carter Wynne Smoot who was a partner in many of his endeavors. He was the ultimate optimist, loved and admired by all who were fortunate to know him.