The finite dynamic system of all possible orientations of a given graph with all accessible states and with inaccesible states
The nite dynamic systems (􀀀G; ) is considered, the states of which are all possible orientations of a given graph G, and the evolutionary function transforms a given state 􀀀!G by reversing all arcs in 􀀀!G that enter into sinks, and there are no other di erences between the given 􀀀!G and the next ( 􀀀!G ) states. We characterize the systems in which all states are accessible and in which there are inaccessible states. Namely, in a nite dynamic system (􀀀G; ) all states are accessible if and only if the (connected) components in the graph G are complete graphs with n vertices for 1 6 n 6 3 and only they. Otherwise, the system under consideration has inaccessible states. The number of graphs forming systems with all accessible states is counted. Namely, the number of graphs G with n vertices that form nite dynamic systems (􀀀G; ), all states of which are accessible, is equal to 1+bn=2c+bn=3c+ b(n􀀀P3)=2c i=1 b(n 2i)=3c. The table is given with the number of graphs with the number of vertices from 1 to 12, forming systems with all accessible states and with inaccessible states.