Restricted Enumerations by the Unit-Subduced-Cycle-Index (USCI) Approach. IV. The Restricted-Subduced-Cycle-Index (RSCI) Method for Enumeration of Kekulé Structures and of Perfect Matchings of Graphs

摘要

Restricted enumerations based on the unit-subduced-cycle-index (USCI) approach (S. Fujita, "Symmetry and Combinatorial Enumeration in Chemistry", Springer-Verlag (1991)) are discussed from a viewpoint of subductions into the C_1-group, where only edges contained in a given skeleton are taken into consideration under a restriction condition that occupation of a common vertex (or occupation of adjacent edges) is avoided. The restriction condition for edge occupation is formulated by introducing territory indicators and territory discriminants so as to give a restricted subduced cycle index (RSCI) for the C_1-group. Thereby, the restricted-subduced-cycle-index (RSCI) method for enumerating Kekulé structures (or equivalently perfect matchings of a graph) is developed as a specialized application of the USCI approach. To show the versatility of the RSCI method, the numbers of Kekulé structures for a dodecahedral skeleton, coronene, dibenzo[b,n]picene, dibenzo[bc,mn]ovalene, dibenzo[fg,op]anthanthrene, dibenzo[hi,sl]ovalene, naphtho[8,1,2-efg]anthanthrene, and fullerene C_(60) are calculated by the RSCI method. Maple programs for the RSCI method are reported as examples of practical calculations.