Academician Andrei Petrovich Ershov (19 April 1931 - 8 December 1988) was one of the Soviet pioneers in the field of theoretical and systems programming, the founder of the Siberian School of Programming. His significant contributions to establishing informatics as a new branch of science and a new phenomenon of the social life are widely recognized both in Russia and abroad. His pioneering works on graph-theory methods in programming are somewhat less well known but equally important and highly regarded by the experts. A.P. Ershov called graphs to be the basic tool for the programmer, and said that graphs possess a vast, inexhaustible power commensurate with the scale of programming tasks. He made a fundamental contribution to graph theory particularly in the area of programming. In this paper, A.P. Ershov's works on graph methods in programming are considered.