Attractors and cyclic states in finite dynamic systems of complete graphs orientations | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2023. № 59. DOI: 10.17223/20710410/59/5

A finite dynamical system is considered, the states of which are all possible orientations of a given complete graph, and the evolution function is given as follows: the dynamic image of a digraph is a digraph obtained from the original one by reorienting all the arcs included in the sinks, there are no other differences between the original digraph and its image. The cyclic states of the system (belonging to attractors) are characterized, a table is given with the number of cyclic states and states that are not cyclic in orientation systems of complete graphs with the number of vertices from 1 to 8 inclusive. The formation of attractors of the system, their type, length is described, a table is given with the corresponding number of attractors in the orientation systems of complete graphs with the number of vertices from 1 to 8 inclusive.