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Superconnected and Hyperconnected Small Degree Transitive Graphs

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Abstract

A graph is said to be superconnected if every minimum vertex cut isolates a vertex. A graph is said to be hyperconnected if each minimum vertex cut creates exactly two components, one of which is an isolated vertex. In this paper, we characterize superconnected or hyperconnected vertex transitive graphs with degree 4 and 5. As a corollary, superconnected or hyperconnected planar transitive graphs are characterized.

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References

  1. Boesch F.: On unreliability polynomials and graph connectivity in reliable network synthesis. J. Graph Theory 10, 339–352 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Boesch F.: Synthesis of reliable networks-a survey. IEEE Trans. Reliable. 35, 240–246 (1986)

    Article  MATH  Google Scholar 

  3. Boesch F., Tindell R.: Circulants and their connectivities. J. Graph Theory 8, 487–499 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  4. Liang C.: The connectivity of vertex-transitive graphs with small regular degrees. J. Xinjing Univ. 4, 5–7 (2000)

    Google Scholar 

  5. Hamidone Y.O.: Subsets with small sums in abelian groups’I: the vosper property. Europ. J. Combin. 4, 541–556 (1997)

    Article  Google Scholar 

  6. Lakshmivaraham S., Jung-Sing J., Dhall S.K.: Symmetry in interconnection networks on Cayley graphs of permutation groups: a survey. Parallel Comput. 19, 361–407 (1993)

    Article  MathSciNet  Google Scholar 

  7. Mader M.: Minimal n-fach Kantenzusammenhangenden Granphen. Math. Ann. 191, 21–28 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  8. Jixiang M.: Connevtivity of vertex and edge transitive graphs. Discrete Appl. Math. 127, 601–613 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Tindell R.: Connectivity of Cayley graphs. In: Du, D.Z., Hsu, D.F. (eds) Combinatorial Network Theory, pp. 41–64. Kluwer, Dordrecht (1996)

    Google Scholar 

  10. Dameng W., Jixiang M.: Superconnected and hyperconnected cubic transitive graphs. OR Trans. 5(4), 35–40 (2001)

    Google Scholar 

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, Xinjiang, People’s Republic of China

    Yingzhi Tian & Jixiang Meng

Authors
  1. Yingzhi Tian
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  2. Jixiang Meng
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Correspondence to Yingzhi Tian.

Additional information

The research is supported by NSFC (No.10671165) and NSFXJ (No. 2010211A06).

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Tian, Y., Meng, J. Superconnected and Hyperconnected Small Degree Transitive Graphs. Graphs and Combinatorics 27, 275–287 (2011). https://doi.org/10.1007/s00373-010-0972-3

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  • DOI: https://doi.org/10.1007/s00373-010-0972-3

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