Graph-theoretical analysis of the sextet polynomial. Proof of the correspondence between the sextet patterns and Kekulé patterns

摘要

Wenjie and Wenchen defined the sextet pattern and the super sextet and claimed to prove the one-to-one correspondence between the Kekulé and sextet patterns 1. However, the set of sextet patterns of a polyhexGby their definition cannot be obtained unless we know all the Kekulé patterns ofG. In this sense, their definition does not match the theory of the sextet polynomial. Here, the whole set of sextet patterns, including the super sextets ofG, is defined from the properties ofG, not from the Kekulé patterns. The one-to-one correspondence between the Kekulé and sextet patterns is thus pro