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Introduction to the Class of Prefractal Graphs

Author

Listed:
  • Rasul Kochkarov

    (Department of Data Analysis and Machine Learning, Faculty of Information Technology and Big Data Analysis, Financial University under the Government of the Russian Federation, Leningradsky Prospekt 49/2, 125167 Moscow, Russia)

  • Azret Kochkarov

    (Department of Data Analysis and Machine Learning, Faculty of Information Technology and Big Data Analysis, Financial University under the Government of the Russian Federation, Leningradsky Prospekt 49/2, 125167 Moscow, Russia
    Moscow Aviation Institute, National Research University, Volokolamskoe shosse 4, 125993 Moscow, Russia)

Abstract

Fractals are already firmly rooted in modern science. Research continues on the fractal properties of objects in physics, chemistry, biology and many other scientific fields. Fractal graphs as a discrete representation are used to model and describe the structure of various objects and processes, both natural and artificial. The paper proposes an introduction to prefractal graphs. The main definitions and notation are proposed—the concept of a seed, the operations of processing a seed, the procedure for generating a prefractal graph. Canonical (typical) and non-canonical (special) types of prefractal graphs are considered separately. Important characteristics are proposed and described—the preservation of adjacency of edges for different ranks in the trajectory. The definition of subgraph-seeds of different ranks is given separately. Rules for weighting a prefractal graph by natural numbers and intervals are proposed. Separately, the definition of a fractal graph as infinite is given, and the differences between the concepts of fractal and prefractal graphs are described. At the end of the work, already published works of the authors are proposed, indicating the main backlogs, as well as a list of directions for new research. This work is the beginning of a cycle of works on the study of the properties and characteristics of fractal and prefractal graphs.

Suggested Citation

  • Rasul Kochkarov & Azret Kochkarov, 2022. "Introduction to the Class of Prefractal Graphs," Mathematics, MDPI, vol. 10(14), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2500-:d:865499
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    References listed on IDEAS

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    Cited by:

    1. Boris V. Rumiantsev & Rasul A. Kochkarov & Azret A. Kochkarov, 2023. "Graph-Clustering Method for Construction of the Optimal Movement Trajectory under the Terrain Patrolling," Mathematics, MDPI, vol. 11(1), pages 1-13, January.

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