MATHEMATICAL FOUNDATIONS OF INFORMATION TECHNOLOGY

Tensor models of fractal graphs for elastic networks

A. Semenov

Moscow Aviation Institute (National Research University), Moscow, Russia

Abstract: The article presents the results of research on fractal (self-similar) graphs in relation to elastic computing. A characteristic feature of such graphs is their ability to unfold (increase dimensionality) and fold (decrease dimensionality). Two approaches to forming fractal graphs are considered: based on Kronecker product and fractal algebra. The interrelationship of algebraic operations of forming fractal graphs (linear graphs, grids, hypercubes, and trees) with tensor operations and tensor representation based on the integration of adjacency matrices and event vectors of elastic systems is presented. Definitions of corresponding types of dynamically changing tensors are introduced. An analysis of the properties of elastic fractal graphs and related tensor models is conducted.

Keywords: Kronecker graphs, fractal graphs, fractal algebra, elastic networks, tensor models.

Language: English

DOI: 10.14357/20718632230412

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