Group-theoretical approach to the investigation of reaction graphs for highly degenerate rearrangements of chemical compounds I. Criterion of the connectivity of a graph

We give a necessary and sufficient condition for a reaction graph of a degenerate rearrangement to be connected. This condition is formulated in terms of vertex stabilizers of the automorphism group of a molecular graph. The condition is illustrated on several examples, including the reaction graph of bullvalene. We consider different mathematical models for the construction of reaction graphs and state the problem: which of the models is more adequate?