On the number of rounds necessary to disseminate information
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
SIAM Journal on Computing
Fast information sharing in a complete network
Discrete Applied Mathematics
Methods and problems of communication in usual networks
Proceedings of the international workshop on Broadcasting and gossiping 1990
Discrete Mathematics
Distributed loop computer networks: a survey
Journal of Parallel and Distributed Computing
A note on isomorphic chordal rings
Information Processing Letters
On the Ádám Conjecture on Circulant Graphs
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
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Knödel graphs and Fibonacci graphs are two classes of bipartite incident-graph of circulant digraphs. Both graphs have been extensively studied for the purpose of fast communications in networks, and they have deserved a lot of attention in this context. In this paper, we show that there exists an O(n log5 n)-time algorithm to recognize Knödel graphs, and that the same technique applies to Fibonacci graphs. The algorithm is based on a characterization of the cycles of length six in these graphs (bipartite incident-graphs of circulant digraphs always have cycles of length six). A consequence of our result is that none of the Knödel graphs are edge-transitive, apart those of 2k -2 vertices. An open problem that arises in this field is to derive a polynomial-time algorithm for any infinite family of bipartite incident-graphs of circulant digraphs indexed by their number of vertices.