Properties and Lemmas

The following three simple properties of fixed bonds are easily proved. 

Property 8.2. An essentially disconnected single coronoid G has a fixed single bond. 

The coronoid G has a fixed bond by definition. If G has a fixed single bond, then there is nothing to prove. If G has a fixed double bond, then the edges incident to this bond must evidently be fixed single bonds. This completes the proof. 

In other words, fixed double bonds are always accompanied by fixed single bonds. From this viewpoint we may say that fixed single bonds are the fiindamental feature of essentially disconnected systems. The simple reasoning of the above proof is applicable to other essentially disconnected systems than single coronoids as well. It has been applied to benzenoids by Chen, Cyvin SJ and Cyvin (1990). 

Property 8.8. A fixed bond cannot be contained in an M-altemating cycle P for a Kekule structure M of G. 

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