Radially Moore graphs of radius three and large odd degree

Extremal graphs which are close related to Moore graphs have been defined in different ways. Radially Moore graphs are one of these examples of extremal graphs. Although it is proved that radially Moore graphs exist for radius two, the general problem remains open. Knor, and independently Exoo, gives some constructions of these extremal graphs for radius three and small degrees. As far as we know, some few examples have been found for other small values of the degree and the radius. Here, we consider the existence problem of radially Moore graphs of radius three. We use the generalized undirected de Bruijn graphs to give a general construction of radially Moore graphs of radius three and large odd degree.Peer Reviewe

Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010

Peer Reviewe