Skip to main content
Springer Nature Link
Log in

A Finite Complete Set of Equations Generating Graphs

  • Conference paper
  • First Online:
Discrete Mathematics and Theoretical Computer Science (DMTCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2731))

Abstract

It was known that every graph can be constructed from a finite list of elementary graphs using the operations of graph sum and graph composition. We determine a complete set of “equations” or rewriting rules with the property that two expressions represent the same graph if and only if one can be transformed into the other by means of these rules.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. A. Arnold and M. Dauchet, Théorie des magmoides. I. RAIRO Inform. Théor. 12(3), 235–257 (1978).

    MATH  MathSciNet  Google Scholar 

  2. A. Arnold and M. Dauchet, Théorie des magmoides. II. RAIRO Inform. Théor. 13(2), 135–154 (1979).

    MATH  MathSciNet  Google Scholar 

  3. M. Bauderon and B. Courcelle, Graph Expressions and Graph Rewritings. Math.Syst.Theory 20, 83–127 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Bossut, M. Dauchet, B. Warin, A Kleene theorem for a class of planar acyclic graphs. Inform. and Comput. 117, 251–265 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  5. V. Claus, Ein Vollständigkeitssatz für Programme und Schaltkreise. Acta Informatica 1, 64–78, (1971).

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Corradini and F. Gadducci, An algebraic presentation of term graphs, via gs-monoidal categories. Appl. Categ. Structures 7(4), 299–331 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  7. V.E. Cazanescu and Gh. Ştefănescu, Towards a new algebraic foundation of flowchart scheme theory. Fundamenta Informaticae, 13, 171–210, (1990).

    MATH  MathSciNet  Google Scholar 

  8. J. Engelfriet and J.J. Vereijken, Context-free graph grammars and concatenation of graphs. Acta Informatica 34, 773–803 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Gibbons, An initial-algebra approach to directed acyclic graphs. Mathematics of program construction (Kloster Irsee, 1995), 282–303, LNCS 947, Springer, Berlin, (1995).

    Google Scholar 

  10. G. Hotz, Eine Algebraisierung des Syntheseproblems von Schaltkreisen. EIK 1, 185–205, 209–231, (1965).

    MathSciNet  MATH  Google Scholar 

  11. G. Hotz, Eindeutigkeit und Mehrdeutigkeit formaler Sprachen. EIK 2, 235–246, (1966).

    MathSciNet  MATH  Google Scholar 

  12. P. Katis, N. Sabadini and R.F.C. Walters, Bicategories of processes. Journal of Pure and Applied Algebra, 115, 141–178, (1997).

    Article  MATH  MathSciNet  Google Scholar 

  13. P. Katis, N. Sabadini and R.F.C. Walters, SPAN(Graph): A categorical algebra of transition systems. In M. Johnson, editor, Algebraic Methodology and Software Technology, volume 1349 of LNCS, pages 307–321 Springer Verlag, 1997.

    Chapter  Google Scholar 

  14. A. Joyal, R.H. Street and D. Verity, Traced monoidal categories. Mathematical Proceedings of the Cambrige Philosophical Society, 119, 425–446, (1996).

    Article  MathSciNet  Google Scholar 

  15. Gh. Ştefănescu, On flowcharts theories: Part II. The nondetermenistic case. Theoret. Comput. Sci., 52, 307–340, (1987).

    Article  MathSciNet  MATH  Google Scholar 

  16. Gh. Ştefănescu, Algebra of flownomials. Technical Report SFB-Bericht 342/16/94 A, Technical University of München, Institut für Informatik, (1994).

    Google Scholar 

  17. Gh. Ştefănescu, Network algebra. Discrete Mathematics and Theoretical Computer Science (London). Springer-Verlag, 400 pp. (2000).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Aristotle University of Thessaloniki, 54006, Thessaloniki, Greece

    Symeon Bozapalidis & Antonios Kalampakas

Authors
  1. Symeon Bozapalidis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonios Kalampakas
    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 Auckland, Maths-Physics Building 303, 38 Princes St., Auckland, New Zealand

    Cristian S. Calude  & Michael J. Dinneen  & 

  2. Université de Bourgogne, LE2I, B.P. 47870, 21078, Dijon Cedex, France

    Vincent Vajnovszki

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bozapalidis, S., Kalampakas, A. (2003). A Finite Complete Set of Equations Generating Graphs. In: Calude, C.S., Dinneen, M.J., Vajnovszki, V. (eds) Discrete Mathematics and Theoretical Computer Science. DMTCS 2003. Lecture Notes in Computer Science, vol 2731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45066-1_9

Download citation

  • DOI: https://doi.org/10.1007/3-540-45066-1_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40505-4

  • Online ISBN: 978-3-540-45066-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation