Protrusive benzenoid

The protrusive benzenoids form a subclass of the extremal benzenoids. By definition a protrusive benzenoid has a formula with no other formula in the same column above it, and no formula in the same row to the left of it in the periodic table. All pericondensed protrusive benzenoids are generated by circumscribing the extremal benzenoids. Consequently they have the formulas as given below [53],... 

In addition comes naphthalene (C10H8), which also by definition is a protrusive benzenoid, the only catacondensed system of this class. 

The extreme-left benzenoids are defined by formulas on the staircase-like boundary so that, in each case, there is no formula in the same row to the left. Hence the extremal benzenoids without benzene form a subclass of the extreme-left benzenoids.But there exist extreme-left benzenoids, say x, which are not extremal. Their formulas are found one step up and one step to the right from every formula for the pericondensed protrusive benzenoids. Hence one obtains readily the following expression. 

The original aufbau principle of Dias [16] (see also above) is not applicable to protrusive benzenoids. Apart from this, it has been formulated for the even-carbon atom systems, but can also be extended immediately to the odd-carbon atom systems. As such this incomplete principle works in most of the relevant cases of Figs. 6 and 7 only C38H16 and C40H16 are counterexamples therein. 

Proposition 3 A protrusive benzenoid with the formula on top of a three-formula step has no bay. 

This proposition is proved straightforwardly in an analogous way to Proposition 2 (a) or (b) the positions of the formulas C HS and C + 2HS are considered. A protrusive benzenoid is also extremal and has consequently neither a cove or a fjord. 

Benzenoid (chemical) isomers are, in a strict sense, the benzenoid systems compatible with a formula C HS. Several invariants, including the Dias parameter, are treated and relations between them are given. Many of the relations involve upper and lower bounds. The periodic table for benzenoid hydrocarbons is revisited and new aspects of it are pointed out. In this connection some new classes of benzenoids are defined extreme-left, protrusive and circular. Extensive tables of enumeration data for benzenoid isomers are presented. Some of their forms are displayed in figures. 

Let again the formulas (n s) and (ri s ) pertain to A and circum-A, respectively, where A is an extremal benzenoid. Then, by virtue of Proposition 5 (Sect. 7.1) it should be clear that circum-A must be protrusive (and hence also extremal). 

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