The high school student in each graduating class in each high school in the state who, upon the completion of four years of high school work in a high school in the state, obtains the highest average standing for all the credits earned, and who is graduated at an annual commencement is entitled to receive, during dormitory residence at the University of Alaska, a scholarship covering dormitory rent for a period of two years following the year of graduation upon presenting to the registrar of the university a certificate signed by the superintendent or principal of the high school from which the student graduated stating that the graduate named is entitled to receive the benefits of the scholarship. Dormitory residence is governed by the rules and regulations established by the Board of Regents.