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(2, 3)-Cordial Trees and Paths

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Combinatorics, Graph Theory and Computing (SEICCGTC 2021)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 448))

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Abstract

Recently L. B. Beasley introduced (2, 3)-cordial labelings of directed graphs in [1]. He conjectured that every orientation of a path of length at least five is (2, 3)-cordial, and that every tree of max degree \(n =3\) has a cordial orientation. In this paper we formally define (2, 3)-cordiality from the viewpoint of quasigroup cordiality. We show both conjectures to be false, discuss the (2, 3)-cordiality of orientations of the Petersen graph, and establish an upper bound for the number of edges a graph can have and still be (2, 3)-orientable.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Utah State University, Logan, Utah, 84322-3900, USA

    Manuel Santana, Jonathan Mousley, Dave Brown & LeRoy B. Beasley

Authors
  1. Manuel Santana
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  2. Jonathan Mousley
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  3. Dave Brown
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  4. LeRoy B. Beasley
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Corresponding author

Correspondence to Manuel Santana .

Editor information

Editors and Affiliations

  1. Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA

    Frederick Hoffman

  2. Mathematics, Kennesaw State University, Kennesaw, GA, USA

    Sarah Holliday

  3. Mathematics, Florida Atlantic University, Boca Raton, FL, USA

    Zvi Rosen

  4. Computer Science and Engineering, University of North Texas, Denton, TX, USA

    Farhad Shahrokhi

  5. Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA

    John Wierman

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© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

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Santana, M., Mousley, J., Brown, D., Beasley, L.B. (2024). (2, 3)-Cordial Trees and Paths. In: Hoffman, F., Holliday, S., Rosen, Z., Shahrokhi, F., Wierman, J. (eds) Combinatorics, Graph Theory and Computing. SEICCGTC 2021. Springer Proceedings in Mathematics & Statistics, vol 448. Springer, Cham. https://doi.org/10.1007/978-3-031-52969-6_12

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