Fiol, M. A.; Gimbert, J.; Miller, M. Multipartite Moore digraphs. (English) Zbl 1105.05028 Linear Algebra Appl. 419, No. 1, 234-250 (2006). Summary: We derive some Moore-like bounds for multipartite digraphs, which extend those of bipartite digraphs, under the assumption that every vertex of a given partite set is adjacent to the same number \(\delta\) of vertices in each of the other independent sets. We determine when a multipartite Moore digraph is weakly distance-regular. Within this framework, some necessary conditions for the existence of an \(r\)-partite Moore digraph with interpartite outdegree \(\delta > 1\) and diameter \(k = 2m\) are obtained. In the case \(\delta = 1\), which corresponds to almost Moore digraphs, a necessary condition in terms of the permutation cycle structure is derived. Additionally, we present some constructions of dense multipartite digraphs of diameter two that are vertex-transitive. 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