Geodesic
The graph of acyclic digraphs
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 4, pp. 441-452

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The paper introduces the concept of a binary reflexive relation of adjacency on the set of all binary relations of a set $X$ (in terms of characteristic functions) and determines an algebraic system consisting of all binary relations of the set and of all unordered pairs of adjacent binary relations. If $X$ is a finite set then this algebraic system is a graph (“the graph of graphs”). It is proved that the diameter of a graph of binary relations is 2. It is shown that if $\sigma$ and $\tau$ are adjacent relations, then $\sigma$ is an acyclic relation (finite acyclic digraph) if and only if $\tau$ is an acyclic relation. An explicit formula for the number of connected components of a graph of acyclic relations is received.
Keywords: binary relation, acyclic digraph. 
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Kh. Sh. Al' Dzhabri; V. I. Rodionov. The graph of acyclic digraphs. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 4, pp. 441-452. http://geodesic.mathdoc.fr/item/VUU_2015_25_4_a0/