Geodesic
An efficient algorithm for finding final vertices in a generalized functional graph
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 1, Tome 238 (2025), pp. 59-68

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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.
Keywords: discrete dynamic system, functional graph, algorithm complexity 
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O. V. Zubkov. An efficient algorithm for finding final vertices in a generalized functional graph. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 6th International Conference "Dynamic Systems and Computer Science: Theory and Applications" (DYSC 2024). Irkutsk, September 16-20, 2024. Part 1, Tome 238 (2025), pp. 59-68. http://geodesic.mathdoc.fr/item/INTO_2025_238_a4/