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Counting Vertices in Iterated Line Graphs

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  • First Online:
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

We introduce new methods of studying properties of iterated line graphs and demonstrate the use of these methods on a class of tree graphs. We also describe plans to generalize these methods further and derive identities for the number of vertices in the iterated line graphs of arbitrary graphs among other potential extensions of the methodology.

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References

  1. Balch, B.: Iterated line graphs on bi-regular graphs and trees. Rose-Hulman Undergrad. Math. J. 21(1) , Article 2 (2020)

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  2. King, Z.: Iterated line graphs of graphs with regular and bi-regular partitions. Unpublished.

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  3. Merris, R.: Graph Theory. Wiley (2001)

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  4. Wiener, N.W.: A Simplification of the Logic of Relations (1912)

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  5. Kathiresan, K.M.: A Study on H-line graphs. Australian J. Combin. 58(3), 358–364 (2014)

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Central Oklahoma, Edmond, OK, 73034, USA

    Zack King, Liz Lane-Harvard & Thomas Milligan

Authors
  1. Zack King
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  2. Liz Lane-Harvard
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  3. Thomas Milligan
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Corresponding author

Correspondence to Liz Lane-Harvard .

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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King, Z., Lane-Harvard, L., Milligan, T. (2024). Counting Vertices in Iterated Line Graphs. 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_27

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