Directed tree structure of the set of Kekulé patterns of generalized polyhex graphs

In this paper the authors define the concept of g-sextet rotation graph of a generalized polyhex graph G, and prove that the g-sextet rotation graph D(G) of G is a directed tree. This conclusion is a generalization of an earlier result and also valid for any polyhex fragment graphs. Furthermore, by the present results, an error in a proof of the Ohkami-Hosoya conjecture about a one-to-one correspondence between Kekulé and sextet patterns of a polyhex graph is corrected.