Skip to main content

On the Energy of Transposition Graphs

  • 293 Accesses

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


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.


  • Transposition graphs
  • Permutation groups
  • Network computing

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions


  1. 1.

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


  1. Akers, S.B., Harel, D., Krishnamurthy, B.: The star graph: An attractive alternative to the \(n\)-cube. Proc. Int. Conf. Parallel Process, 393–400 (1987).

    Google Scholar 

  2. Akers S. B., Krishnamurthy, B.: A group-theoretic model for symmetric interconnection networks, IEEE Trans. Comput. 38, 555–566 (1989).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Bacher, R.: Valeur propre minimale du laplacien de Coxeter pour le groupe symétrique. J. Algebra, 167(2), 460–472 (1994).

    CrossRef  MathSciNet  Google Scholar 

  4. Biggs, N.: Algebraic Graph Theory. Cambridge University Press, England (2001).

    MATH  Google Scholar 

  5. Cheng, E., Liptak, L., Shawash, N.: Orienting Cayley graphs generated by transposition trees. Computers and Mathematics with App 55 (11) 2662–2672 (2008).

    CrossRef  MathSciNet  Google Scholar 

  6. Day, K., Tripathi, A.: A comparative study of topological properties of hypercubes and star graphs. IEEE Trans. Comput., 5(1), 31–38 (1994).

    MathSciNet  Google Scholar 

  7. Graovac, A., Gutman, I., Trinajsti, N., Topological Approach to the Chemistry of Conjugated Molecules, Springer, Berlin (1977).

    CrossRef  Google Scholar 

  8. Gutman, I., Polansky, O.E.: Mathematical Concepts in Organic Chemistry, Springer, Berlin (1986).

    CrossRef  Google Scholar 

  9. Gutman, I., Trinajstic N., Graph theory and molecular orbitals. Topics Curr. Chem. 42(49), (1973).

    Google Scholar 

  10. Harary, F., Schwenk, A.J.: Which graphs have integral spectra? In: Graphs and Combinatorics (Lecture Notes in Mathematics 406, ed. R. Bari, F. Harary), Springer-Verlag, Berlin-Heidelberg-New York pp. 45–51 (1974).

    Google Scholar 

  11. Heydemann, M.C., Ducourthial, B.: Cayley graphs and interconnection networks. In: G. Hahn, G. Sabidussi, Graph Symmetry, NATO Advanced Science Institutes Series C. In: Mathematica and Physical Sciences, Kluwer Academic Publishers, Dordrecht, 497, 167–224 (1997).

    Google Scholar 

  12. Krakovski R., Mohar B.: Spectrum of Cayley graphs on the symmetric group generated by transpositions. arXiv:1201.2167, 201

  13. Labarre, A.: Combinatorial Aspects of Genome Rearrangements and Haplotype Networks/Aspects (Combinatoires Des Réarrangements Génomiques Et Des Réseaux D’haplotypes). Ph.D. Thesis, Université Libre De Bruxelles (2008).

    Google Scholar 

  14. Lakshmivarahan, S., Jwo, J.S., Dhall, S.: Symmetry in interconnection networks based on Cayley graphs of permutation groups: a survey. Parallel Computing, 19, 361–407 (1993).

    CrossRef  MathSciNet  Google Scholar 

  15. Latifi, S., Srimani, P.K.: Transposition networks as a class of fault-tolerant robust networks, IEEE Trans. Comput. 230–238 (1996).

  16. Shi, Ling-Sheng, and Peng Wu. Conditional Connectivity of Bubble Sort Graphs. Acta Mathematicae Applicatae Sinica, English Series, 33(4), 933–944 (2017).

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to M. R. DeDeo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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.

Download citation