Search for the bullvalene-like structures

A new way to formalize the description of [3,3]-sigmatropic rearrangement in annulenes is suggested. The straightforward procedure to search for bullvalene-like annulenes is described in terms of graph theory. The transformation of a chemical graph to its homomorphic image allows description of the Cope rearrangement as a redistribution of labels on the edges of a homomorphic graph. Two selection criteria are suggested for evaluation of the topological possibility of degenerate Cope rearrangements, which are followed by equalization of carbon and hydrogen atoms. The results of the exhaustive search for the bullvalene-like structures among the planar annulenes are presented and discussed, as well as for 6–18 vertex homomorphic images of non-planar annulene structures. The results of a brute-force attempt to find the analogy of bullvalene among the C_n (n=6,8) families are also briefly described.