In November 1966, he joined the 2nd Replacement Company, Staging Battalion, Marine Corps Base, Camp Pendleton, California, for transfer to the Republic of Vietnam.

The President of the United States in the name of The Congress takes pride in presenting the MEDAL OF HONOR posthumously to for service as set forth in the following CITATION: For conspicuous gallantry and intrepidity at the risk of his life above and beyond the call of duty as Commanding Officer, Company F, Second Battalion, Fifth Marines, First Marine Division, in the Republic of Vietnam on 2 June 1967.

Resolute to silence the second machine-gun, which continued its devastating fire, Captain Graham's small force stood steadfast in its hard won enclave.

Subsequently, during the afternoon's fierce fighting, he suffered two minor wounds while personally accounting for an estimated fifteen enemy killed.

The last radio transmission from Captain Graham reported that he was being assaulted by a force of twenty-five enemy; he died while protecting himself and the wounded man he chose not to abandon.

His outstanding courage, superb leadership and indomitable fighting spirit undoubtedly saved the second platoon from annihilation and reflected great credit upon himself, the Marine Corps, and the United States Naval Service.