Skip to main content
Log in

Algebraic operations on graphs with using numeric coding for simulating the systems of rocket and space technology

  • Flight Vehicle Design
  • Published:
Russian Aeronautics Aims and scope Submit manuscript

Abstract

The paper adduces the relators for algebraic operations on graphs using the numeric codes of the graphs. The special algebra of codes has been devised with consideration of the principles of graph transformation. This paper demonstrates the relevance of numeric coding of graphs for solving the problems of enumeration, systematization, and compact representation of the information about the structural and functional characteristics of the systems of flow distribution and conversion of rocket and space technology and for conducting the modeling transformations of given systems in the course of the structural and functional studies as well.

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.

Similar content being viewed by others

References

  1. Gravchenko, Yu.A., Grankin, B.C., and Kozlov, V.V., Synthesis of Functional Structure of Power Flow Systems in Support Equipment of the Rocket and Space Technology, Trudy vserossiiskoi nauchnoprakticheskoi konferentsii “Sovremennye problemy uluchsheniya taktiko-tekhnicheskikh charakteristik raketnokosmicheskoi tekhniki, ee sozdaniya, ispytanii i ekspluatatsii” (Proc. the All Russian Scientific and Practical Conference “The Current Problems of Improving the Tactic and Technical Characteristics of Rocket and Space Technology, Its Production, Testing, and Operation”), St. Petersburg, 2014, vol. 1, pp. 94–99.

    Google Scholar 

  2. Gravchenko, Yu.A., Grankin, B.C., and Kozlov, V.V., Synthesis Automation for Functional Structure of Power Flow Systems in Support Equipment of the Rocket and Space Technology, Trudy vserossiiskoi nauchnoprakticheskoi konferentsii “Sovremennye problemy uluchsheniya taktiko-tekhnicheskikh charakteristik raketnokosmicheskoi tekhniki, ee sozdaniya, ispytanii i ekspluatatsii” (Proc. the All Russian Scientific and Practical Conference “The Current Problems of Improving the Tactic and Technical Characteristics of Rocket and Space Technology, Its Production, Testing, and Operation”), St. Petersburg, 2014, vol. 1, pp. 100–104.

    Google Scholar 

  3. Gravchenko, Yu.A., Grankin, B.C., Kozlov, V.V., and Mokan, D.O., Structural and Functional Aspect of Studying the Technical Systems of the Rocket and Space Systems, Trudy VKA im. A.F. Mozhaiskogo, 2014, issue 644, pp. 153–156.

    Google Scholar 

  4. Gravchenko, Yu.A., Grankin, B.C., Kukushkin, I.O., and Mokan D.O., Graph Coding for Solving the Problems of Power Flow Distribution and Conversion, Trudy VKA im. A.F. Mozhaiskogo, 2015, issue 649, pp. 23–28.

    Google Scholar 

  5. Buslenko, N.P., Modelirovanie slozhnykh system (Simulation of Complex Systems), Moscow: Nauka, 1968.

    Google Scholar 

  6. Kontorov, D.S. and Golubev-Novozhilov, Yu.S., Vvedenie v radiolokatsionnuyu sistemotekhniku (Introduction into Radar System Engineering), Moscow: Sovetskoe Radio, 1971.

    Google Scholar 

  7. Miller, R.E., Switching Theory, John Wiley and Sons, 1965.

    Google Scholar 

  8. Mason, S.J., Feedback Theory—Some Properties of Signal Flow Graphs, Proceedings of the IRE, 1953, vol. 41, no. 9, pp. 1144–1156.

    Article  Google Scholar 

  9. Shatikhin, L.G., Strukturnye matritsy i ikh primenenie dlya issledovaniya sistem (Structural Matrices and Their Application for System Investigation), Moscow: Mashinostroenie, 1974.

    MATH  Google Scholar 

  10. Nechiporenko, V.I., Strukturnyi analiz i metody postroeniya nadezhnykh system (Structural Analysis and Methods of Constructing the Reliable Systems), Moscow: Sovetskoe Radio, 1968.

    Google Scholar 

  11. Manheim, M.L., Hierarchical Structure: A Model of Design and Planning Processes, The MIT Press, 1967.

    Google Scholar 

  12. Bellert, S. and Wozniacki, H., Analysis and Synthesis of Electrical Systems by Means of the Method of Structural Numbers, Warszawa: PWN, 1968.

    Google Scholar 

  13. Trokhimenko, Ya.K., Metod obobshchennykh chisel i analiz lineinykh tsepei (Method of Generalized Numbers and Analysis of Linear Circuits), Moscow: Sovetskoe Radio, 1972.

    Google Scholar 

  14. Kovalev, M.A., A Method for Automation of a Process of Aircraft Hydraulic System Modeling, Izv.Vuz. Av. Tekhnika, 2009, vol. 45, no. 3. pp. 44–49 [Russian Aeronautics (Engl.Transl)), vol. 45, no. 3, pp. 62–11].

    Google Scholar 

  15. Kovalev, M.A., Tensor Representation of Structure of Aircraft Hydraulic Systems, Izv.Vuz. Av. Tekhnika, 2009, vol. 45, no. 4. pp. 64–67 [Russian Aeronautics (Engl.Transl)), vol. 45, no. 4, pp. 474–479].

    Google Scholar 

  16. Harary, F., Graph Theory, Boston: Addison-Wesley Publishing Co., 1969.

    Book  MATH  Google Scholar 

  17. Ore, O., Theory of Graphs, American Mathematical Society, 1962.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. V. Chirva.

Additional information

Original Russian Text © Yu.A. Gravchenko, B.K. Grankin, V.V. Kozlov, S.V. Chirva, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Aviatsionnaya Tekhnika, 2017, No. 3, pp. 8–14.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gravchenko, Y.A., Grankin, B.K., Kozlov, V.V. et al. Algebraic operations on graphs with using numeric coding for simulating the systems of rocket and space technology. Russ. Aeronaut. 60, 327–334 (2017). https://doi.org/10.3103/S1068799817030023

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068799817030023

Keywords

Navigation