Journal of Mathematical Sciences

, Volume 134, Issue 5, pp 2354–2357 | Cite as

On the vertex connectivity of a relation in an association scheme

  • S. A. Evdokimov
  • I. N. Ponomarenko


We prove that for a sufficiently closed association scheme, the Brouwer conjecture on the coincidence of the vertex connectivity and the degree of any its connected basis relation is true. Bibliography: 7 titles.


Basis Relation Association Scheme Vertex Connectivity Connected Basis 
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  1. 1.
    A. E. Brouwer, “Spectrum and connectivity of graphs},” CWI Quarterly}, 9}, 37–40 (199Google Scholar
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    A. E. Brouwer and D. M. Mesner, “The connectivity of strongly regular graphs},” European J. Combin.}, 6}, 215–216 (198Google Scholar
  3. 3.
    S. Evdokimov and I. Ponomarenko, “Separability number and schurity number of coherent configurations},” Electron. J. Combin.}, 7}, #R31 (200Google Scholar
  4. 4.
    S. Evdokimov and I. Ponomarenko, “Characterization of cyclotomic schemes and normal Schur rings over a cyclic group},” Algebra Analiz}, 14}, 11–55 (200Google Scholar
  5. 5.
    S. Evdokimov, M. Karpinski, and I. Ponomarenko, “On a new high dimensional Weisfeiler-Leman algorithm},” J. Algebraic Combin.}, 10}, 29–45 (199Google Scholar
  6. 6.
    S. Evdokimov, I. Ponomarenko, and G. Tinhofer, “Forestal algebras and algebraic forests (on a new class of weakly compact graphs)},” Discrete Math.}, 225}, 149–172 (200Google Scholar
  7. 7.
    M. Watkins, “Connectivity of transitive graphs},” J. Combin. Theory}, 8}, 23–29 (197Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • S. A. Evdokimov
    • 1
  • I. N. Ponomarenko
    • 2
  1. 1.St.Petersburg Institute for Informatics and AutomationSt.PetersburgRussia
  2. 2.St.Petersburg Department of the Steklov Mathematical InstituteRussia

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