An efficient algorithm for finding final vertices in a generalized functional graph

In the paper, 2-outgoing graphs are introduced into consideration, generalizing functional graphs and modeling discrete dynamic systems of a special type. The vertices and arcs of a 2-outgoing graph are classified, paths on these graphs are defined, and some properties of these paths are proved. As a result, an efficient algorithm is constructed that, with linear complexity, constructs final vertices for paths starting at each of the vertices of a 2-outgoing graph, and its correctness is proven.