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On Recognizing Cayley Graphs

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Algorithms - ESA 2000 (ESA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1879))

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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.

This work is supported by an Australian-French cooperation granted by CNRS and ARC. Part of this work has been done while the three first authors were visiting the Department of Computing of Macquarie University, Sydney. Additional support by Spanish Research Council (CICYT) under project TIC97-0963, by the CNRS, and by the Aquitaine Region project #98024002.

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Author information

Authors and Affiliations

  1. Departament de Matemàtica Aplicada i Telemàtica, Univ. Politécnica de Catalunya, Campus Nord, Edifici Jordi Girona 1-2, 08034, Barcelona, Spain

    Lali Barrière

  2. Laboratoire de Recherche en Informatique, Bât. 490, 91405, Orsay, France

    Pierre Fraigniaud

  3. Laboratoire Bordelais de Recherche en Informatique, 33405, Talence, France

    Cyril Gavoille & John M. Robson

  4. Department of Computing, Macquarie Univ., Sydney, NSW, 2109, Australia

    Bernard Mans

Authors
  1. Lali Barrière
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  2. Pierre Fraigniaud
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  3. Cyril Gavoille
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  4. Bernard Mans
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  5. John M. Robson
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK

    Mike S. Paterson

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© 2000 Springer-Verlag Berlin Heidelberg

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Barrière, L., Fraigniaud, P., Gavoille, C., Mans, B., Robson, J.M. (2000). On Recognizing Cayley Graphs. In: Paterson, M.S. (eds) Algorithms - ESA 2000. ESA 2000. Lecture Notes in Computer Science, vol 1879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45253-2_8

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  • DOI: https://doi.org/10.1007/3-540-45253-2_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41004-1

  • Online ISBN: 978-3-540-45253-9

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