Core coronoid

This relation indicates that is not a core coronoid. This class of coronoids is defined in... 

In Fig. 4.2 (cf. also Fig. 2) all the systems in the top and bottom rows are core benzenoids or core simple coronoids. The two first systems in the middle row (viz. C24H12 and C32H14) are not core benzenoids, while the last system therein (viz. C66H22) is a non-core single coronoid. There exist core coronoids of different natures, as is explained below. 

Firstly, if an excised coronoid Cq, viz. c(Cq), is not itself a coronoid, then the circumscribing of c(Cq) is not defined, and Cq becomes automatically a core coronoid. The two last systems of the top and bottom rows of Fig. 4.2 (viz. C32H16 and C48H20) examples. In particular, every catacondensed coronoid is a core coronoid belonging to the category under consideration. If Q is a catacondensed single coronoid vdthout an inside feature (cf. Vol. I), then e(Q) consists of the inner perimeter of Q. 

If a coronoid has a furing edge it must necessarily be a core coronoid. Notice also that all fusing edges disappear from a coronoid as soon as it is circumscribed (if possible). Finally it is noted that c(Cq) very well may be a non-core coronoid even if Cq is a core coronoid. An example is shown below. 

It is clear that Cq is a core coronoid if the conditions of Observation 5.3 are fulfilled. But also, if a coronoid C has no fusing edge and e(C) is a coronoid, it is inferred that C is restored by circumscribing c(C) one only has to recall the mechanism of excising and circumscribing. 

The class of reproducible core coronoids (analogous with the reproducible core benzenoids) is especially important. A reproducible core coronoid Cq fulfils the condition that... 

Corollary 5.2. If Aq is an extremal core single coronoid, then c(Aq) is not a coronoid. 

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