Groupe d’études et de recherche en analyse des décisions

G-93-20

Bonds Fixed by Fixing Bounds

et

In a normal benzenoid hydrocarbon H no bonds are fixed, i.e. each bond belongs to some perfect matching or Kekulé structure of H. Fixing one of the bonds of H implies the fixation of several other ones. Several results related to such bonds fixed by fixing bonds are obtained: (a) previous algorithms for finding in linear time a Kekulé structure of a benzenoid hydrocarbon H (or showing it has none) and for finding all fixed bonds of H are generalized to obtained all bonds fixed by fixing each of the bonds of H in O(N2) time where N is the number of carbon atoms of H; (b) the fixation graph, which expresses fixation of bonds from bonds fixed, and the symmetry graph are introduced and used to find the Pauling bond orders of all edges of H; (c) a characterization is given of fixable benzenoids, which possess a bond whose fixing implies the fixation of all other bonds.

, 27 pages