Abstract
Generalized de Bruijn and Kautz networks are important since they allow networks of any size with vertices of fixed degree. Communication issues are related to easy construction/enumeration of shortest paths between vertex-couples. An easy method based on residue calculation is introduced to find multiple shortest paths if they exist, allowing better communication schemes. The main results concern the properties of multiple shortest paths (especially disjunction) and the number of vertex-couples separated by several shortest paths as a function of the graph size. Conditions to get or avoid networks with multiple shortest paths are proposed which can be useful for the design of communication schemes.
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