On central trees of a graph

  • S. Shinoda
  • T. Kawamoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 108)


The concept of central trees of a graph has attracted our attention in relation to electrical network theory. Until now, however, only a few properties of central trees have been clarified. In this paper, in connection with the critical sets of the edge set of a graph, some new theorems on central trees of the graph are presented. Also, a few examples are included to illustrate the applications of these theorems.


Central Tree Tokyo Institute Circuit Theory Engineer Faculty Hybrid Equation 
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  1. [1]
    N. Deo: A central tree, IEEE Trans. Circuit Theory; Vol. CT-13, pp.439–440, 1960.Google Scholar
  2. [2]
    N. R. Malik: On Deo's central tree concept; IEEE Trans. Circuit Theory, Vol. CT-15, pp.283–284, 1968.Google Scholar
  3. [3]
    V. Amoia and G. Cottafava: Invariance properties of central trees; IEEE Trans. Circuit Theory, Vol. CT-18, pp,465–467, 1971.Google Scholar
  4. [4]
    G. Kishi and Y. Kajitani: Generalized topological degree of freedom in analysis of LCR networks; Papers of the Technical Group on Circuit and System Theory of Inst. Elec. Comm. Eng. Japan, No.CT 71-19, pp.1–13, July 1971.Google Scholar
  5. [5]
    Y. Kajitani: The semibasis in network analysis and graph theoretical degree of freedom; IEEE Trans. Circuits and Systems, Vol.CAS-26, pp.846–854, 1979.Google Scholar
  6. [6]
    T. Kawamoto, Y. Kajitani and S. Shinoda: New theorems on central trees described in connection with the principal partition of a graph, Papers of the Thchnical Group on Circuit and System Theory of Inst. Elec. Comm. Eng. Japan, No.CST77-109, pp. 63–69, Dec. 1977.Google Scholar
  7. [7]
    S. Shinoda, M. Kitano and C. Ishida: Two theorems in connection with partitions of graphs; Papers of the Technical Group on Circuits and Systems of Inst. Elec. Comm. Eng. Japan, No.CAS79-146, pp.1–6, Jan. 1980.Google Scholar
  8. [8]
    S. Shinoda and K. Saishu: Conditions for an incidence set to be a central tree, ibid., No.CAS80-6, pp. 41–46, Apr. 1980.Google Scholar
  9. [9]
    G. Kishi and Y. Kajitani: On maximally distinct trees, Proceedings of the Fifth Annual Allerton Conference on Circuit and System Theory, University of Illinois, pp.635–643, Oct. 1967.Google Scholar
  10. [11]
    S. Shinoda: Principal partitions of graphs with applications to graph and network problems, Proc. of Inst. Elec. Comm. Eng. Japan, Vol.62, pp.763–772, 1979.Google Scholar
  11. [12]
    N. Tomizawa: Strongly irreducible matroids and principal partitions of a matroid into strongly irreducible minors, Trans. Inst. Elec. comm. Eng. Japan, Vol. J59-A, pp.83–91, 1976.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • S. Shinoda
    • 1
  • T. Kawamoto
    • 2
  1. 1.Department of Electrical Engineering Faculty of Science and EngineeringChuo UniversityKasuga, Bunkyo-ku, TokyoJapan
  2. 2.Department of Electrical and Electronic Engineering Faculty of EngineeringTokyo Institute of TechnologyO-okayama, Meguro-ku, TokyoJapan

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