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Parallel structures in multidimensional networks

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Abstract

The method of parallel representation of networks is used to determine the restrictions imposed by the space dimension on the variety of multidimensional regular networks. The method makes it possible to establish an analytic relation between the network dimension and the connectivity of vertices and the perimeter of elementary contours. It is proved that an infinite-dimensional network is equivalent to an infinite tree. In addition, the problem of closed regular polytopes inside networks is discussed.

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Authors and Affiliations

  1. Blagonravov Mechanical Engineering Research Institute, Russian Academy of Sciences, ul. Bardina 4, Moscow, 119334, Russia

    V. V. Smolyaninov

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  1. V. V. Smolyaninov
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Original Russian Text © V.V. Smolyaninov, 2006, published in Biofizika, 2006, Vol. 51, No. 6, pp. 1106–1133.

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Smolyaninov, V.V. Parallel structures in multidimensional networks. BIOPHYSICS 51, 971–995 (2006). https://doi.org/10.1134/S0006350906060170

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  • DOI: https://doi.org/10.1134/S0006350906060170

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