Half essentially disconnected

Whereas the scheme in Sect. 2.1 applies to both benzenoids and single coronoids, a finer classification for the Kekulean single coronoids was found to be needed during the studies of Kekul6 structure counts for these systems. In this way the concept half essentially disconnected (single) coronoids was introduced by Cyvin SJ, Cyvin and Brunvoll (1987). This concept is explained in the book of Gutman and Cyvin (1989) and in Vol. 1-3.3. 

Fig. 2.1. One regular (r), one half essentially disconnected (he), and one essentially disconnected (c) single coronoid. Numbers K of Kekule structures are indicated.

The HED coronoid depicted in Sect. 2.2, as well as the systems of the same category (he) in Figs. 1 and 3, are all examples of half essentially disconnected coronoids with isolated (nonadjacent) internal vertices. Notice that the colors of the internal vertices alternate successively as white-black—white—black—. when going around the corona hole cf. the left-hand colunm of the below diagram. 

It was also confirmed that the Kekule structure count is the same for the two isospectral systems under consideration K = 12636. It is interesting that the pair of systems consists of one half essentially disconnected (HED) and one essentially disconnected single coronoid. The two schemes of Kekule structures for the HED system (left-hand drawing in Chart 4) are indicated below. 

Abbreviations hr bridged catacondensed c essentially disconnected he half essentially disconnected o non—Kekulean rp regular pericondensed. 

In Sect. 2.2 the half essentially disconnected (HED) single coronoids are defined (provisionally) as the normal single coronoid which are not regular. A direct definition of the HED single coronoids, compatible with the provisional definition of Sect. 2.2, is furnished through the theorem of the next paragraph. 

Definition 8.8 A normal single coronoid G is half essentially disconnected (HED) if and only if —... 

Cyvin SJ, Cyvin BN, BrunvoU J (1987) Half Essentially Disconnected Coronoid Hydrocarbons. Chem Phys Letters 140 124... 

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