THEOREMS FOR SINGLE CORONOIDS

In this chapter some graph—theoretical proofs are conducted for generalized single coronoids. Some of these proofs are closely connected with the discussion of Sect. 2.2. In particular, the rheo conjecture is proved. 

Benzenoids and coronoids can be generated (or built up) by additions of hexagons to the perimeters (Vol. 1-2.1.1 Cyvin BN, Brunvoll and Cyvin 1992b) see also Par. 6.5.1. The addition modes are Li, P2 Pi a nd L5, indicating the mode which the added hexagon acquires after the addition (cf. Table 6.4). For coronoids we also need the coronor-condensation which is an addition of a hexagon into the mode L2 or A2 so that a corona hole is created. 

Definitions 8.1 A normal addition is an addition (of a hexagon) into the mode Li, L3 or L5. A regular addition is either a normal addition or a corona-condensation. 

Hence a regular addition is associated with the mode Li, L2, A2,13 or i/5. The opposite process of a normal (resp. regular) addition is a normal (resp. regular) tearing down. 

---