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Corona Product Complexity of Planar Graph and S-chain Graph

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Networked Systems (NETYS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 9944))

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Abstract

Since its appearance, the number of spanning trees of a graph has been among the most important problems in graph theory. We aimed to get explicit formula counting this number in the corona product graph of two planar graphs. In this paper, we study the corona product of a planar graph with a linear chain and cycle chain, for which we calculate their number of spanning trees. Our research findings highlight the potential of combinatorial method, which allowed us to count this number for a large graph as corona product graph.

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References

  1. Kirchhoff, G.G.: Über die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Strme gefhrt wird. Ann. Phys. Chem. 72, 497–508 (1847)

    Article  Google Scholar 

  2. West, D.B.: Introduction to Graph Theory, 2nd edn. University of Illinois, Urbana (2002)

    Google Scholar 

  3. Yakoubi, F., El Marraki, M.: Enumeration of spanning trees in certain vertex corona product graph. Appl. Math. Sci. 8(109), 5427–5438 (2014)

    Article  Google Scholar 

  4. Sedlacek, J.: On the skeletons of a graph or digraph. In: Proceedings of Calgary International Conference of Combinatorial Structures and Their Applications, Gordon and Breach, pp. 387–391 (1970)

    Google Scholar 

  5. Modabish, A., El Marraki, M.: The number of spanning trees of certain families of planar maps. Appl. Math. Sci. 5(18), 883–898 (2011)

    MathSciNet  MATH  Google Scholar 

  6. Al Etaiwi, clar:ekeW.M.: Encryption algorithm using graph theory. J. Sci. Res. Rep. 3(19), 2519–2527 (2014). Article No: JSRR.2014.19.004

    Google Scholar 

  7. Lotfi, D., El Marraki, M., Aboutajdine, D.: The contraction method for counting the complexity of planar graphs with cut vertices. Appl. Math. Sci. 7(70), 3479–3488 (2013)

    Article  MathSciNet  Google Scholar 

  8. Colbourn, C.J.: The Combinatorics of Network Reliability. Oxford University Press, New York (1980)

    Google Scholar 

  9. Myrvold, W., Cheung, K.H., Page, L.B., Perry, J.E.: Uniformly-most reliable networks do not always exist. Networks 21, 417–419 (1991)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. LRIT Associated Unit the CNRST (URAC29), Faculty of Sciences, University of Mohammed V, P.O. Box 1014, Rabat, Morocco

    Fouad Yakoubi & Mohamed El Marraki

Authors
  1. Fouad Yakoubi
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  2. Mohamed El Marraki
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Corresponding author

Correspondence to Fouad Yakoubi .

Editor information

Editors and Affiliations

  1. Uppsala University , Uppsala, Sweden

    Parosh Aziz Abdulla

  2. Université Paris Diderot , Paris, France

    Carole Delporte-Gallet

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Yakoubi, F., El Marraki, M. (2016). Corona Product Complexity of Planar Graph and S-chain Graph. In: Abdulla, P., Delporte-Gallet, C. (eds) Networked Systems. NETYS 2016. Lecture Notes in Computer Science(), vol 9944. Springer, Cham. https://doi.org/10.1007/978-3-319-46140-3_30

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  • DOI: https://doi.org/10.1007/978-3-319-46140-3_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46139-7

  • Online ISBN: 978-3-319-46140-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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