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On Recognizing Cayley Graphs

  • Lali Barrière
  • Pierre Fraigniaud
  • Cyril Gavoille
  • Bernard Mans
  • John M. Robson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1879)

Abstract

Given a class C of Cayley graphs, and given an edge-colored graph G of n vertices and m edges, we are interested in the problem of checking whether there exists an isomorphism φ preserving the colors such that G is isomorphic by φ to a graph in C colored by the elements of its generating set. In this paper, we give an O(m log n)-time algorithm to check whether G is color-isomorphic to a Cayley graph, improving a previous O(n 4.752 log n) algorithm. In the case where C is the class of the Cayley graphs defined on Abelian groups, we give an optimal O(m)-time algorithm. This algorithm can be extended to check color-isomorphism with Cayley graphs on Abelian groups of given rank. Finally, we propose an optimal O(m)-time algorithm that tests color-isomorphism between two Cayley graphs on ℤn, i.e., between two circulant graphs. This latter algorithm is extended to an optimal O(n)-time algorithm that tests colorisomorphism between two Abelian Cayley graphs of bounded degree.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Lali Barrière
    • 1
  • Pierre Fraigniaud
    • 2
  • Cyril Gavoille
    • 3
  • Bernard Mans
    • 4
  • John M. Robson
    • 3
  1. 1.Departament de Matemàtica Aplicada i TelemàticaUniv. Politécnica de CatalunyaBarcelonaSpain
  2. 2.Laboratoire de Recherche en Informatique, Bât. 490OrsayFrance
  3. 3.Laboratoire Bordelais de Recherche en InformatiqueTalenceFrance
  4. 4.Department of ComputingMacquarie Univ.SydneyAustralia

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