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"Dualities" in graph theory and in the related fields viewed from the metatheoretical standpoint

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 108)

Abstract

The importance is emphasized of distinguishing clearly among different kinds of concepts usually referred to as "duality". Those different kinds of dualities concentrate in the "dual graph", wherefrom confusion is sometimes given rise to. The importance is illustrated by "new" theorems and concepts which are derived by understanding correctly the difference of the concepts.

Keywords

Duality Theorem Dual Graph Triangular Inequality Dual Structure Admittance Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    Iri, M.: Metatheoretical considerations on duality. RAAG Research Notes, Third Series, No. 124, February 1968.Google Scholar
  2. [2]
    Iri, M.: Network Flow, Transportation and Scheduling — Theory and Algorithms. Academic Press, New York, 1969.Google Scholar
  3. [3]
    Iri, M.; Recski, A.: Reflection on the concepts of dual, inverse and adjoint networks (in Japanese). Papers of the Technical Group on Circuits and Systems, Institute of Electronics and Communication Engineers of Japan, CAS 79–78 (September 1979). (English translation available)Google Scholar
  4. [4]
    Iri, M.; Recski, A.: Reflection on the concepts of dual, inverse and adjoint networks, II — Towards a qualitative theory (in Japanese). Papers of the Technical Group on Circuits and Systems, Institute of Electronics and Communication Engineers of Japan, CAS 79–133 (January 1980). (English translation available)Google Scholar
  5. [5]
    Kemeny, J. G.: A new approach to semantics — Part I; Part II. Journal of Symbolic Logic, Vol. 21, No. 1 (March 1956), pp. 1–27; No. 2 (June 1956), pp. 149–161.Google Scholar
  6. [6]
    Robinson, A.: On the Metamathematics of Algebra. North-Holland Publishing Co., Amsterdam, 1951.Google Scholar
  7. [7]
    Smullyan, R. M.: First-Order Logic. Springer-Verlag, Berlin, 1968.Google Scholar
  8. [8]
    Berge, C.: Graphes et Hypergraphes. Dunod, Paris, 1970.Google Scholar
  9. [9]
    Pontrjagin, L.: Topological Groups. Princeton University Press, Princeton, 1946.Google Scholar
  10. [10]
    Lefschetz, S.: Algebraic Topology. American Mathematical Society Colloquium Publications, Vol. 27, New York, 1942.Google Scholar
  11. [11]
    Iri, M.: Linear Programming (in Japanese). Hakujitsu-sha, Tokyo, 1973.Google Scholar
  12. [12]
    Berge, C.; Ghouila-Houri, A.: Programmes, Jeux et Réseaux de Transport. Dunod, Paris, 1962.Google Scholar
  13. [13]
    Ford, L. R., Jr.; Fulkerson, D. R.: Flows in Networks, Princeton University Press, Princeton, 1962.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • M. Iri
    • 1
  1. 1.Department of Mathematical Engineering and Instrumentation Physics Faculty of EngineeringUniversity of TokyoHongo, Bunkyo-ku, TokyoJapan

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