A New Approach to Operating with Undirected Trees


A new approach has been developed and practically implemented in the created software package. It ensures the implementation, on undirected trees, of a wide set of basic operations that allows replenishment. The approach does not require the development and use of available types of formalized representation of trees (matrices of adjacency, connectivity, incidence, distance, adjacency lists, etc.), standardized description languages, and specialized programs for constructing and visualization tools for their structure. By reducing the cost of technical resources and time when solving problems from various fields of knowledge by dozens (and hundreds) of times, the approach makes the work as simple and effective as possible, allows us to obtain a number of characteristics that are important in practical terms, to solve the problem of tree isomorphism, and to generate two options of representing the adjacency matrix.

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  1. 1.

    A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley Longman Publishing Co., Inc., Reading, Mass. (1974).

  2. 2.

    V. A. Emelichev, O. I. Melnikov, V. I. Sarvanov, and R. I. Tyszkiewicz, Lectures on the Graph Theory [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  3. 3.

    V. A. Evstigneev and V. N. Kasyanov, Graph Theory: Algorithms for Tree Processing [in Russian], Nauka, Novosibirsk (1994).

    Google Scholar 

  4. 4.

    C. M. Hoffmann, Group-Theoretics Algorithms and Graph Isomorphism; Lecture Notes in Computer Science, Vol. 136, Berlin–Heidelberg, Springer-Verlag (1982).

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Correspondence to A. I. Ivaneshkin.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2021, pp. 142–152.

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Ivaneshkin, A.I. A New Approach to Operating with Undirected Trees. Cybern Syst Anal 57, 124–132 (2021). https://doi.org/10.1007/s10559-021-00335-z

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  • graph tree
  • undirected tree
  • isomorphism
  • a set of software tools