Reaction Graphs

Chemical reaction graphs (for a fixed type of rearrangement) are orbital graphs for transitive permutation representations of symmetric groups, so algebraic combinatorics and group theory are effective tools for studying such properties as their connectivity and automorphisms. For example, we construct orbital graphs (and, hence, reaction graphs) from Cayley diagrams by contracting edges, and use graph-embeddings in surfaces to determine the automorphism groups of these graphs. We apply these ideas to the rearrangements of the P₇^3--ion and of bullvalene, together with some purely mathematical examples of reaction graphs.