[2] After joining the Australian Army in January 1938,[3] at the age of 19 he graduated from the Royal Military College, Duntroon (RMC) in August 1940, following the outbreak of the Second World War.

[5] During an action on the morning of 17 April C Company, under Graham's command, encountered heavy resistance in thick jungle while attacking strong Japanese positions around Andersons Junction, astride Dawe Creek.

Personally leading the attack, he placed a number of anti-tank guns to cover a river crossing and following heavy fighting the Australians finally secured a foothold by late in the afternoon which allowed a bridge to be erected across the creek for the tanks to move forward in support.

[13] Following the war, Graham served in various staff positions in Eastern Command based in New South Wales, and in 1946 he was posted to Japan on the Headquarters of the British Commonwealth Occupation Force.

[5] Graham attended the United States Armed Forces Staff College and subsequently filled the role of Assistant Military Attaché in Washington, D.C. as an intelligence officer in 1957–58.

[1][17] After being promoted to colonel, he served as Director of Military Intelligence between 1960 and 1964, and while the Australian Army was developing its own doctrine on counter-revolutionary warfare, Graham's ideas on counter-insurgency were influenced by a visit to South Vietnam in November 1961.

[4][19] On 1 January 1967 Graham was appointed Commander 1st Australian Task Force (1 ATF) which was based in Phuoc Tuy Province, South Vietnam, taking over from Brigadier David Jackson.

[4] According to Ian McNeill and Ashley Ekins, the official historians of Australian involvement in the Vietnam War, Graham quickly established himself, and developed a sound operational concept, yet the Viet Cong succeeded in preventing him from implementing it as he had intended.

[20] With just two battalions 1 ATF's ability to generate combat power was severely limited, while its location at Nui Dat isolated it from the main population centres and increased the burden of self-protection.

[20] To Graham such losses underscored the need for a third infantry battalion and tanks, yet with the Australian government unable to provide additional military resources at that time, they confirmed in his mind the need to establish a physical barrier to deny the Viet Cong freedom of movement.

However, recognising the threat the obstacle posed to them, the Viet Cong had immediately begun attempting to penetrate it, cutting gaps in the fence and clearing lanes through the minefield to restore the flow of supplies, as well as lifting mines for their own use.

[27] While in keeping with the orthodoxy of Australian counter-insurgency doctrine, Graham's strategy ultimately proved both controversial and costly, and despite initial success, the minefield became a source of munitions for the Viet Cong and later the decision was made to remove it amid growing casualties.

[28] Yet such flaws were not immediately obvious and by the second half of 1967 the Viet Cong in Phuoc Tuy Province seemed to have melted away, abandoning many of their bunker systems and avoiding the main roads and towns.

[29] He reasoned that a succession of operations in the south-east of the province and the completion of the barrier minefield at Dat Do meant that no single, sizable threat remained to the populated areas of Phuoc Tuy.

[31] Graham believed that the large public turnout in Phuoc Tuy had been due to the long-term effects of Australian operations in the province which had increased the population's sense of security.

[34] By 1969 a large percentage of Australian casualties in Vietnam were being caused by mines, including significant quantities of M16 anti-personnel devices removed by the Viet Cong from the barrier minefield at Dat Do.

[4] Meanwhile, after visiting Phuoc Tuy Province respected journalist Denis Warner concluded that although the original concept in laying the minefield had been sound, it was ultimately one of the greatest Australian mistakes of the war.

[3] Despite the debate surrounding the laying of the barrier minefield, McNeill and Ekins later described Graham as a "clever and imaginative" commander, who was "widely regarded as having one of the best minds in the army", and whose "broad knowledge and fair approach earned him the respect of his subordinates.