Skip to main content
SpringerLink
Log in

(k+) -Disatance- Herediatry Graphs

(Extended abstract)

  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2204))

Included in the following conference series:

Abstract

In this work we introduce, characterize, and provide algorithmic results for (k, +)-distance-hereditary graphs. These graphs can be used to model interconnection networks with desirable connectivity properties; a network modeled as a (k, +)-distance-hereditary graph can be characterized as follows: if some nodes have failed, as long as two nodes remain connected, the distance between these nodes in the faulty graph is bounded by k plus the distance in the non-faulty graph. The class of all these graphs is denoted by DH(k, +) By varying the parameter k, classes DH(k, +) form a hierarchy that represents a parametric extension of the well-known class of distance-hereditary graphs, and include all graphs.

Work partially supported by the Italian MURST Project “Teoria dei Grafi ed Applicazioni”.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. J. Bandelt and M. Mulder. Distance-hereditary graphs. Journal of Combinatorial Theory, Series B, 41(2):182–208, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Brandstädt, V. B. Le and J. P. Spinrad. Graph classes — a survey. SIAM Monographs on Discrete Mathematics and Applications, Philadelphia, 1999.

    Google Scholar 

  3. J. Bruck, R. Cypher, and C.-T. Ho. Fault-tolerant meshes with small degree. SIAM J. on Computing, 26(6):1764–1784, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Cicerone and G. Di Stefano. Graph classes between parity and distancehereditary graphs. Discrete Applied Mathematics, 95(1-3): 197–216, August 1999.

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Cicerone, G. Di Stefano, and M. Flammini. Compact-Port routing models and applications to distance-hereditary graphs. In 6th Int. Colloquium on Structural Information and Communication Complexity (SIROCCO’99), pages 62–77, Carleton Scientific, 1999.

    Google Scholar 

  6. S. Cicerone and G. Di Stefano. Graphs with bounded induced distance. Discrete Applied Mathematics, 108(1-2): 3–21, January 2001.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Cicerone and G. Di Stefano. Networks with small stretch number. In Proc. 26th International Workshop on Graph-Theoretic Concepts in Computer Science, WG2000, pages 95–106. Lecture Notes in Computer Science, vol. 1928, Springer-Verlag, 2000.

    Chapter  Google Scholar 

  8. S. Cicerone, G. Di Stefano, and D. Handke. Survivable networks with bounded delay: The edge failure case (Extended Abstract). In Proc. 10th Annual International Symp. Algorithms and Computation, ISAAC’99, pages 205–214. Lecture Notes in Computer Science, vol. 1741, Springer-Verlag, 1999.

    Google Scholar 

  9. G. D’Ermiliis. Topologie di reti con particolari caratteristiche metriche. Master thesis, Faculty of Engineering, University of L’Aquila, 2000.

    Google Scholar 

  10. G. Di Stefano. A routing algorithm for networks based on distance-hereditary topologies. In 3rd Int. Colloquium on Structural Information and Communication Complexity (SIROCCO’96), 1996.

    Google Scholar 

  11. A. H. Esfahanian and O. R. Oellermann. Distance-hereditary graphs and multidestination message-routing in multicomputers. Journal of Comb. Math. and Comb. Computing, 13:213–222, 1993.

    MATH  MathSciNet  Google Scholar 

  12. A. M. Farley and A. Proskurowski. Self-repairing networks. Parallel Processing Letters, 3(4):381–391, 1993.

    Article  MathSciNet  Google Scholar 

  13. M.R. Garey and D.S. Johnson. Computers and Intractability. A Guide to the Theory of NP-completeness. W.H. Freeman, 1979.

    Google Scholar 

  14. J. P. Hayes. A graph model for fault-tolerant computing systems. IEEE Transactions on Computers, C-25(9):875–884, 1976.

    Article  MathSciNet  Google Scholar 

  15. E. Howorka. Distance hereditary graphs. Quart. J. Math. Oxford, 2(28):417–420, 1977.

    Article  MathSciNet  Google Scholar 

  16. F. T. Leighton, B. M. Maggs, and R. K. Sitaraman. On the fault tolerance of some popular bounded-degree networks. SIAM J. on Computing, 27(6):1303–1333, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  17. D. Peleg and A. Schaffer. Graph spanners. Journal of Graph Theory, 13:99–116, 1989.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Elettrica, Università dell’Aquila, I-67040, Monteluco di Roio - L’Aquila, Italy

    Serafino Cicerone, Gianluca D’Ermiliis & Gabriele Di Stefano

Authors
  1. Serafino Cicerone
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gianluca D’Ermiliis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gabriele Di Stefano
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rostock, 18051, Rostock, Germany

    Andreas Brandstädt  & Van Bang Le  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cicerone, S., D’Ermiliis, G., Di Stefano, G. (2001). (k+) -Disatance- Herediatry Graphs. In: Brandstädt, A., Le, V.B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2001. Lecture Notes in Computer Science, vol 2204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45477-2_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-45477-2_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42707-0

  • Online ISBN: 978-3-540-45477-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation