### On the extremal regular directed graphs without commutative diagrams and their applications in Coding Theory and Cryptography.

*V. Ustimenko*

#### Abstract

We use term regular directed graph (r. d. g.) for the graph of irreflexive binary relation with the constant number outputs (or inputs) for each vertex. The paper is devoted to studies of maximal size $E_R(d, v)$ of r. d. g. of order $v$ without commutative diagrams formed by two directed passes of length $

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