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Southeastern International Conference on Combinatorics, Graph Theory, and Computing

SEICCGTC 2020: Combinatorics, Graph Theory and Computing pp 305–316Cite as

On the Energy of Transposition Graphs

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 388)

Abstract

We analyze and compare properties of Cayley graphs of permutation graphs called transposition graphs as this family of graphs has better degree and diameter properties than other families of graphs. Cayley graphs are directly related to the properties of its generator set and thus Cayley graphs of permutation groups generated by transpositions inherit almost all of the properties of the hypercube. In particular, we study properties of the complete transportation, (transposition) star graph, bubble-sort graph, modified bubble-sort graph and the binary hypercube and use these properties to determine bounds on the energy of these graphs.

Keywords

  • Transposition graphs
  • Permutation groups
  • Network computing

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Notes

  1. 1.

    \(ST_{n}\) should not be confused with the Star Graph \(S_{k} = K_{1,k}\).

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Authors and Affiliations

  1. University of North Florida, Jacksonville, 32224, USA

    M. R. DeDeo

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  1. M. R. DeDeo
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Correspondence to M. R. DeDeo .

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Editors and Affiliations

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

    Frederick Hoffman

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DeDeo, M.R. (2022). On the Energy of Transposition Graphs. In: Hoffman, F. (eds) Combinatorics, Graph Theory and Computing. SEICCGTC 2020. Springer Proceedings in Mathematics & Statistics, vol 388. Springer, Cham. https://doi.org/10.1007/978-3-031-05375-7_23

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