Skip to main content
SpringerLink
Log in

The truncation of a cage graph

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

The modern nanotechnology applies various cage molecules having a polyhedral shape. Topologically, a polyhedron is represented by its map. Since such a map is a plane graph, one may apply various graph-theoretical methods also for studying polyhedra. Of similar use are molecular (multi)tori. The surface of a multitorus is locally plane and allows one to apply much the same mathematical methods. This text is an introduction into the spectral theory of truncated cage graphs and truncated multitori. It anticipates further extensions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. D. Cvetković, Spectra of graphs formed by some unary operations. Publ. Inst. Math. 19(33), 37–41 (1975)

    Google Scholar 

  2. D.M. Cvetković, M. Doob, I. Gutman, A. Torgašev, Recent Results in the Theory of Graph Spectra (North-Holland, Amsterdam, 1988)

    Google Scholar 

  3. R. Murugavel, M. Bhattacharjee, H.W. Roesky, Review. Organosilanetriols: Model compounds and potential precursors for metal-containing silicate assemblies. Appl. Organomet. Chem. 13, 227–243 (1999)

    Article  CAS  Google Scholar 

  4. M.V. Diudea, I. Gutman, L. Jantschi, Molecular Topology (Nova Science Publishers, New York, 2001)

    Google Scholar 

  5. V.R. Rosenfeld, On mathematical engineering and design of novel molecules for nanotechnological applications—review. Sci. Isr. Technol. Adv. 9(1), 56–65 (2007)

    CAS  Google Scholar 

  6. V.R. Rosenfeld, Toward molecules with nonstandard symmetry’, in: Diamond and Related Nanostructures, ed. by M.V. Diudea and C.L. Nagy (Springer, Berlin, 2013), Ch. 14, p. 275–285

  7. V.R. Rosenfeld, T.E. Nordahl, Semigroup theory of symmetry. J. Math. Chem. 54(9), 1758–1776 (2016)

    Article  CAS  Google Scholar 

  8. F. Harary, Graph Theory (Addison-Wesley Publishing Company Inc, Reading, 1969)

    Google Scholar 

  9. M.V. Diudea, Multi-Shell Polyhedral Clusters (Springer, Berlin, 2016). (in preparation)

    Google Scholar 

  10. D.M. Cvetković, M. Doob, H. Sachs, Spectra of Graphs-Theory and Application (VEB Deutscher Verlag der Wissenschaften, Berlin, 1980)

    Google Scholar 

Download references

Acknowledgements

We are grateful to our anonymous reviewers for their useful remarks and positive evaluation of the manuscript. The support of the Ministry of Absorption of the State Israel (through fellowship “Shapiro”) is acknowledged.

Author information

Authors and Affiliations

  1. Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, Arany Janos Str. 11, 400028, Cluj, Romania

    Mircea V. Diudea

  2. Department of Computer Science and Mathematics, Ariel University, 40700, Ariel, Israel

    Vladimir R. Rosenfeld

Authors
  1. Mircea V. Diudea
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir R. Rosenfeld
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir R. Rosenfeld.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Diudea, M.V., Rosenfeld, V.R. The truncation of a cage graph. J Math Chem 55, 1014–1020 (2017). https://doi.org/10.1007/s10910-016-0716-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-016-0716-6

Keywords

Search

Navigation