The Maximum Points and Spanning Paths of a Directed Complete Graph

LANDAU proved that the distance from a point with maximum outdegree to any other point is 1 or 2 in a directed complete graph G. Nevertheless, the converse of this theorem does not hold. Namely, even if the distance from a point e of G to any other point is 1 or 2, the point e has not always the maximum outdegree. Then, in this article, extending the theorem of LANDAU, we call a point e of G a "maximum point" of G if the distance from e to any other point is 1 or 2, and we denote by max G the set of all maximum points of G. The propose of this article is to study some properties of the set max G and of spanning paths of a directed complete graph G. This article is based on my paper [4] that is polished and improved.