Multipartite Moore digraphs

Multipartite Moore Digraphs

We derive some Moore-like bounds for multipartite digraphs, which extend those of bipartite digraphs, assuming that every vertex of a given partite set is adjacent to the same number of vertices (δ) in each of the other independent sets. We determine when a Moore multipartite digraph is weakly distanceregular. Within this framework, some necessary conditions for the existence of a Moore r-parti...

On Moore bipartite digraphs

In the context of the degree/diameter problem for directed graphs, it is known that the number of vertices of a strongly connected bipartite digraph satisfies a Moore-like bound in terms of its diameter k and the maximum out-degrees (d1; d2) of its partite sets of vertices. It has been proved that, when d1d2 > 1, the digraphs attaining such a bound, called Moore bipartite digraphs, only exist w...

Kings in semicomplete multipartite digraphs

A digraph obtained by replacing each edge of a complete p-partite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicom-plete p-partite digraph, or just a semicomplete multipartite digraph. A semicomplete multipartite digraph with no cycle of length two is a multipartite tournament. In a digraph D, an r-king is a vertex q such that every vertex in D ...

Cycles in Semicomplete Multipartite Digraphs

Further results on almost Moore digraphs

The nonexistence of digraphs with order equal to the Moore bound Md;k = 1+d+: : :+d k for d; k > 1 has lead to the study of the problem of the existence ofàlmost' Moore digraphs, namely digraphs with order close to the Moore bound. In 1], it was shown that almost Moore digraphs of order Md;k ? 1, degree d, diameter k (d; k 3) contain either no cycle of length k or exactly one such cycle. In thi...