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Large Networks of Diameter Two Based on Cayley Graphs

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Cybernetics and Mathematics Applications in Intelligent Systems (CSOC 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 574))

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Abstract

In this contribution we present a construction of large networks of diameter two and of order \(\frac{1}{2}d^2\) for every degree \(d\ge 8\), based on Cayley graphs with surprisingly simple underlying groups. For several small degrees we construct Cayley graphs of diameter two and of order greater than \(\frac{2}{3}\) of Moore bound and we show that Cayley graphs of degrees \(d\in \{16,17,18,23,24,31,\dots ,35\}\) constructed in this paper are the largest currently known vertex-transitive graphs of diameter two.

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Acknowledgements

The research was supported by VEGA Research Grant No. 1/0811/14 and by the Operational Programme ‘Research & Development’ funded by the European Regional Development Fund through implementation of the project ITMS 26220220179.

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Authors and Affiliations

  1. Faculty of Materials Science and Technology in Trnava, Institute of Applied Informatics, Automation and Mechatronics, Slovak University of Technology in Bratislava, Trnava, Slovak Republic

    Marcel Abas

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  1. Marcel Abas
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Correspondence to Marcel Abas .

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Editors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín Faculty of Applied Informatics, Zlín, Czech Republic

    Radek Silhavy

  2. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Roman Senkerik

  3. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zuzana Kominkova Oplatkova

  4. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zdenka Prokopova

  5. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Petr Silhavy

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Abas, M. (2017). Large Networks of Diameter Two Based on Cayley Graphs. In: Silhavy, R., Senkerik, R., Kominkova Oplatkova, Z., Prokopova, Z., Silhavy, P. (eds) Cybernetics and Mathematics Applications in Intelligent Systems. CSOC 2017. Advances in Intelligent Systems and Computing, vol 574. Springer, Cham. https://doi.org/10.1007/978-3-319-57264-2_23

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  • DOI: https://doi.org/10.1007/978-3-319-57264-2_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57263-5

  • Online ISBN: 978-3-319-57264-2

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