Recognizing Knödel graphs

Authors:
Johanne Cohen;Pierre Fraigniaud;Cyril Gavoille
Affiliations:
LORIA,Campus Scintifique, BP239, 54506 Vandæuvre les Nancy, France;Laboratoire de Recherche en Informatique, University Paris-Sud,Bâtiment 490, 91405 Orsay cedex, France;Laboratoire Bordelais de Recherche en Informatque, University Bordeaux I, 33405 Talence cedex,France
Venue:
Discrete Mathematics
Year:
2002

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Abstract

Knödel graphs form a class of bipartite incident-graph of circulant digraphs. This class has been extensively studied for the purpose of fast communications in networks, and it has 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 of order 2n. 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 the circulant digraphs whose chords are the power of two minus one can be recognized in O(n log5 n) time.