Symmetry properties of chemical graphs VIII. On complementarity of isomerization modes

Abstract

Isomerization mode defines the process of interconversion of one isomer into another. Several mechanisms are conceivable for degenerate rearrangements and, in general, lead to a distinctive network of relations between participating isomers. Here we consider selected modes which are complementary in the sense that if mode 1 transforms an isomer A into B, C, D etc., then mode 2 transforms the same isomer A into X, Y, Z, etc., which includes all isomers not comprised by the first mode. Physico-chemical complementarity can be translated into mathematical complementarity of associated chemical graphs. This allows us to use the tool of Graph Theory. One example of graph theoretical use is the theorem that graph G and its complement G have the same automorphism group (i.e., the same symmetry). We have shown that a close examination of a graph and its complement and their components allows us to recognize the automorphism group in some complex cases without resorting to canonical numbering or other involved procedures, and even allows us to determine isomorphism of different processes.