2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125685In this paper we show a correspondence between directed graphs and bipartite undirected graphs with a perfect matching, that allows to study properties of directed graphs through the properties of the corresponding undirected graphs. In particular it is shown that a directed graph is transitive iff a corresponding undirected graph is Cohen-Macaulay.20 pagesCommutative AlgebraCombinatoricstext