On mixed Moore graphs Original Research Article

The Moore bound for a directed graph of maximum out-degree d and diameter k is image. It is known that digraphs of order image (Moore digraphs) do not exist for image and image. Similarly, the Moore bound for an undirected graph of maximum degree d and diameter k is image. Undirected Moore graphs only exist in a small number of cases. Mixed (or partially directed) Moore graphs generalize both undirected and directed Moore graphs. In this paper, we shall show that all known mixed Moore graphs of diameter image are unique and that mixed Moore graphs of diameter image do not exist.