Skip to main content
Log in

Fast Recognition of Fibonacci Cubes

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

Fibonacci cubes are induced subgraphs of hypercubes based on Fibonacci strings. They were introduced to represent interconnection networks as an alternative to the hypercube networks. We derive a characterization of Fibonacci cubes founded on the concept of resonance graphs. The characterization is the basis for an algorithm which recognizes these graphs in O(mlog n) time.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dedó, E., Torri, D., Zagaglia Salvi, N.: The observability of the Fibonacci cubes. Discret. Math. 255, 55–63 (2002)

    Article  MATH  Google Scholar 

  2. Hsu, W.J.: Fibonacci cubes—a new interconnection topology. IEEE Trans. Parallel Distrib. Syst. 4, 3–12 (1993)

    Article  Google Scholar 

  3. Imrich, W., Klavžar, S.: A convexity lemma and expansion procedures for bipartite graph. Eur. J. Comb. 19, 677–685 (1998)

    Article  MATH  Google Scholar 

  4. Imrich, W., Klavžar, S.: Product Graphs: Structure and Recognition. Wiley, New York (2000)

    MATH  Google Scholar 

  5. Jha, P.K., Slutzki, G.: Convex-expansions algorithms for recognition and isometric embedding of median graphs. Ars Comb. 34, 75–92 (1992)

    MATH  MathSciNet  Google Scholar 

  6. Klavžar, S.: On median nature and enumerative properties of Fibonacci-likes cubes. Discret. Math. 299, 145–153 (2005)

    Article  Google Scholar 

  7. Klavžar, S., Peterin, I.: Projection vectors and Fibonacci and Lucas cubes. Publ. Math. Debr. (to appear)

  8. Klavžar, S., Žigert, P.: Fibonacci cubes are the resonance graphs of fibonaccenes. Fibonacci Quart. 43, 269–276 (2005)

    MathSciNet  Google Scholar 

  9. Klavžar, S., Gutman, I., Mohar, B.: Labeling of benzenoid systems which reflects the vertex-distance relations. J. Chem. Inf. Comput. Sci. 35, 590–593 (1995)

    Article  Google Scholar 

  10. Klavžar, S., Vesel, A., Žigert, P., Gutman, I.: Binary coding of Kekulé structures of catacondensed benzenoid hydrocarbons. Comput. Chem. 25, 569–575 (2001)

    Article  Google Scholar 

  11. Klavžar, S., Vesel, A., Žigert, P.: On resonance graphs of catacondensed hexagonal graphs: structure, coding, and Hamilton path algorithm. MATCH Commun. Math. Comput. Chem. 49, 100–116 (2003)

    Google Scholar 

  12. Klavžar, S., Žigert, P., Brinkmann, G.: Resonance graphs of catacondensed even ring systems are median. Discret. Math. 253, 35–43 (2002)

    Article  Google Scholar 

  13. Liu, J., Hsu, W.-J., Chung, M.J.: Generalized Fibonacci cubes are mostly Hamiltonian. J. Graph Theory 18, 817–829 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mulder, H.M.: The structure of median graphs. Discret. Math. 24, 197–204 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  15. Munarini, E., Zagaglia Salvi, N.: Structural and enumerative properties of the Fibonacci cubes. Discret. Math. 255, 317–324 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  16. Munarini, E., Perelli Cippo, C., Zagaglia Salvi, N.: On the Lucas cubes. Fibonacci Quart. 39, 12–21 (2001)

    MATH  MathSciNet  Google Scholar 

  17. Randić, M.: Resonance in catacondensed benzenoid hydrocarbons. Int. J. Quantum Chem. 63, 585–600 (1997)

    Article  Google Scholar 

  18. Randić, M., Klein, D.J., El-Basil, S., Calkins, P.: Resonance in large benzenoid hydrocarbons. Croat. Chem. Acta 69, 1639–1660 (1996)

    Google Scholar 

  19. Vesel, A.: Characterization of resonance graphs of catacondensed hexagonal graphs. MATCH Commun. Math. Comput. Chem. 53, 195–208 (2005)

    MATH  MathSciNet  Google Scholar 

  20. Wasserman, H.C., Ghozati, S.A.: Generalized linear recursive networks: topological and routing properties. Comput. Electr. Eng. 29, 121–134 (2003)

    Article  MATH  Google Scholar 

  21. Winkler, P.M.: Isometric embeddings in products of complete graphs. Discret. Appl. Math. 7, 221–225 (1984)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrej Taranenko.

Additional information

A. Vesel supported by the Ministry of Science of Slovenia under the grant 0101-P-297.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Taranenko, A., Vesel, A. Fast Recognition of Fibonacci Cubes. Algorithmica 49, 81–93 (2007). https://doi.org/10.1007/s00453-007-9026-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-007-9026-5

Keywords

Navigation