Being the bravest and noblest knight, King Edward, who was childless, looked at him as a potential heir. Graham's father was proud that he was chosen to succeed the aging king. Unfortunately Graham's father did not live to see that event, having died during a border war when Graham was still young. Years later, just after Graham turned nineteen, he was indeed asked by the venerable King to recover Daventry's treasures that had been stolen from him during the years o his reign. Right when Graham returned to the castle after recovering the treasures, the King's heart failed him, and Graham was named king of Daventry.
Source: King's Quest Wikia, "Graham," available under the CC-BY-SA License.