As the German ground forces advanced across the Ukraine in August and September, the air units of JG 52 kept pace – constantly moving on to forward airbases. The "Gruppe" was involved in providing cover for the southern crossings over the Dnieper, the capture of Poltava, the First Battle of Kharkov and then crossing the Perekop isthmus into the Crimea. They often flew three or four missions a day when weather permitted. By the end of October Graf was mastering his flying technique, becoming adept at low-level flying, and had achieved 20 victories. The rains arrived in November, turning the airfields to mud and limiting air operations and the number of serviceable aircraft. Graf's unit was moved forward to Taganrog to support the battle for Rostov. Once the snow arrived, freezing the ground, operations picked up again. In heavy combat over and around the see-saw battle, Graf had doubled his score to 42 by the end of 1941, making him one of the "Gruppe’s" leading pilots. On New Year's Day 1942, III./JG 52 was transferred to the relative comfort of the large Kharkov-Rogan airfield, with its closed hangars. The blizzard conditions (often getting down to −20 °C overnight) made flying virtually impossible. On 24 January, Graf was awarded the Knight's Cross of the Iron Cross for his victories to date. Soon after, he was sent on rotation back home on leave. Within a month, his regular wingman, Steinbatz, was also awarded the Knight's Cross for a similar score.