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Conditional Matching Preclusion Sets for an Mixed-Graph of the Star Graph and the Bubble-Sort Graph

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Intelligent Computing Theories and Methodologies (ICIC 2015)

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Abstract

The conditional matching preclusion number of a graph is the minimum number of edges, whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. Any such optimal set is called an optimally conditional matching preclusion set. The conditional matching preclusion number is one of the parameters to measure the robustness of interconnection networks in the event of edge failure. The star graph and the bubble-sort graph are one of the attractive underlying topologies in a multiprocessor system. In this paper, we investigate a class of Cayley graphs which are combined with the star graph and the bubble-sort graph, and give all the optimally conditional matching preclusion sets for this class of graphs.

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References

  1. Akers, S.B., Krishnamurthy, B.: A group-theoretic model for symmetric interconnection networks. IEEE Trans. Comput. 38(4), 555–566 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bondy, J.A., Murty, U.S.R.: Graph Theory. Springer, New York (2007)

    MATH  Google Scholar 

  3. Brigham, R.C., Harary, F., Violin, E.C., Yellen, J.: Perfect-matching preclusion. Congr. Numerantium 174, 185–192 (2005)

    MathSciNet  Google Scholar 

  4. Cheng, E., Lipták, L.: Matching preclusion for some interconnection networks. Networks 50(2), 173–180 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cheng, E., Lesniak, L., Lipman, M.J., Lipták, L.: Matching preclusion for alternating group graphs and their generalizations. Int. J. Found. Comput. Sci. 19(6), 1413–1437 (2008)

    Article  Google Scholar 

  6. Cheng, E., Lesniak, L., Lipman, M.J., Lipták, L.: Conditional matching preclusion sets. Inf. Sci. 179(8), 1092–1101 (2009)

    Article  Google Scholar 

  7. Cheng, E., Philip, H., Jia, R., Lipták, L.: Matching preclusion and conditional matching preclusion for bipartite interconnection networks II: cayley graphs generated by transposition trees and hyperstars. Networks 59, 357–364 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cheng, E., Lipman, M.J., Lipták, L., Sherman, D.: Conditional matching preclusion for the arrangement graphs. Theor. Comput. Sci. 412, 6279–6289 (2011)

    Article  MATH  Google Scholar 

  9. Cheng, E., Lipták, L., Hsu, L., Tan, J.J.M., Lin, C.: Conditional Matching Preclusion for the Star Graph, Ars Combinatoria (to appear)

    Google Scholar 

  10. Curran, S.J., Gallian, J.A.: Hamiltonian cycles and paths in cayley graphs and digraphs-a survey. Discrete Math. 156(1–3), 1–18 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  11. Thomas, W.: Hungerford: Algebra. Springer-Verlag, New York (1974)

    MATH  Google Scholar 

  12. Li, H., Yang, W., Meng, J.: Fault-tolerant hamiltonian laceability of cayley graphs generated by transposition trees. Discrete Math. 312(21), 3087–3095 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lovász, L., Plummer, M.D.: Matching Theory. Elsevier Science Publishing Company, New York (1986)

    MATH  Google Scholar 

  14. Park, J.-H.: Matching preclusion problem in restricted HL-graphs and recursive circulant G(2 m, 4). J. Kiss 35(2), 60–65 (2008)

    Google Scholar 

  15. Park, J.-H., Son, S.H.: Conditional matching preclusion for hypercube-like interconnection networks. Theor. Comput. Sci. 410, 2632–2640 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, S., Wang, R., Lin, S., Li, J.: Matching Preclusion for k-ary n-cubes. Discrete Appl. Math. 158(18), 2066–2070 (2010)

    Article  MathSciNet  Google Scholar 

  17. Mujiangshan, W., Zhen, W., Shiying, W.: Conditional matching preclusion for bubble-sort graphs. J. Xinjiang Univ. 28(1), 23–35 (2011). (Natural Science Edition) (Chinese Series)

    Google Scholar 

  18. Wang, M., Yang, W., Wang, S.: Conditional matching preclusion number for the cayley graph on the symmetric group. Acta Mathematicae Applicatae Sinica 36(5), 813–820 (2013). (Chinese Series)

    MathSciNet  Google Scholar 

  19. Wang, M., Yang, W., Wang, S.: Optimally conditional matching preclusion sets for a class of cayley graphs on the symmetric group. Chin. J. Eng. Math. 30(6), 901–910 (2013). (Chinese Series)

    Google Scholar 

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Acknowledgements

This work is supported by the National Science Foundation of China (61370001, U1304601)

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Yunxia Ren & Shiying Wang

Authors
  1. Yunxia Ren
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  2. Shiying Wang
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Correspondence to Shiying Wang .

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Editors and Affiliations

  1. Tongji University, Shanghai, China

    De-Shuang Huang

  2. Polytecnic of Bari, Bari, Italy

    Vitoantonio Bevilacqua

  3. University of Wollongong, North Wollongong, New South Wales, Australia

    Prashan Premaratne

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Ren, Y., Wang, S. (2015). Conditional Matching Preclusion Sets for an Mixed-Graph of the Star Graph and the Bubble-Sort Graph. In: Huang, DS., Bevilacqua, V., Premaratne, P. (eds) Intelligent Computing Theories and Methodologies. ICIC 2015. Lecture Notes in Computer Science(), vol 9225. Springer, Cham. https://doi.org/10.1007/978-3-319-22180-9_63

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  • DOI: https://doi.org/10.1007/978-3-319-22180-9_63

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22179-3

  • Online ISBN: 978-3-319-22180-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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