Enumeration of connected components of acyclic digraph. (3rd October 2021) - Al'Dzhabri, Kh. Sh.
Abstract: We established the concept of a binary reflexive relation of adjacency and determined the algebraic system consisting of all binary relations of set X and all unordered pairs of binary relations in terms of characteristic functions on the set of all binary relations of the set X . We investigated some properties of algebraic system of the structure of acyclic digraph. Also, we prove that if σ and τ are adjacent relations, then σ is acyclic relation (finite acyclic digraph) if and only if τ is an acyclic relation. Finally, the number of connected components of an acyclic relations graph is given an exact formula.