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On Extremal Graph Theory, Explicit Algebraic Constructions of Extremal Graphs and Corresponding Turing Encryption Machines

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Artificial Intelligence, Evolutionary Computing and Metaheuristics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 427))

Abstract

We observe recent results on the applications of extremal graph theory to cryptography. Classical Extremal Graph Theory contains Erdős Even Circuite Theorem and other remarkable results on the maximal size of graphs without certain cycles. Finite automaton is roughly a directed graph with labels on directed arrows. The most important advantage of Turing machine in comparison with finite automaton is existence of “potentially infinite memory”. In terms of Finite Automata Theory Turing machine is an infinite sequence of directed graphs with colours on arrows. This is a motivation of studies of infinite families of extremal directed graphs without certain commutative diagrams. The explicite constructions of simple and directed graphs of large girth (or large cycle indicator) corresponds to efficient encryption of Turing machines.

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Authors and Affiliations

  1. Maria Curie-Skłodowska University in Lublin, Pl. Marii Curie-Skłodowskiej 5, Lublin, Poland

    Vasyl Ustimenko & Urszula Romańczuk

  2. Institute of Telecommunications and Global Information Space, Kiev, National Academy of Science of Ukraine, Chokolovsky Boulevard 13, Kiev, Ukraine

    Vasyl Ustimenko

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  1. Vasyl Ustimenko
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  2. Urszula Romańczuk
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  1. , Mathematics and Scientific Computing, National Physical Laboratory, Hampton Road, Teddington, TW11 0LW, United Kingdom

    Xin-She Yang

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Ustimenko, V., Romańczuk, U. (2013). On Extremal Graph Theory, Explicit Algebraic Constructions of Extremal Graphs and Corresponding Turing Encryption Machines. In: Yang, XS. (eds) Artificial Intelligence, Evolutionary Computing and Metaheuristics. Studies in Computational Intelligence, vol 427. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29694-9_11

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  • DOI: https://doi.org/10.1007/978-3-642-29694-9_11

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