### G-93-20

# Bonds Fixed by Fixing Bounds

## and BibTeX reference

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*(*N*^{2}) 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.

Published **July 1993**
,
27 pages