The existence of molecular graphs

Later on we need existence criteria for connected moleculeu- graphs. R. Grund [94,95] deduced the following important existence theorem formulated in terms of valences  

23 Theorem (Existence of molecular graphs in RC) For /S e there exists at least one molecular graph M with if and only if 

For the existence of at least one connected molecular graph we also need (Con) Zxe Zxe P(X)+2 0. This condition is necessary, since a connected 

The given arguments show that the three conditions are necessary for the existence of a connected molecular graph. The proof that they are also sufficient is more important and complicated, we refer to Grund [95]. We denote the set of molecular formulas satisfying (Grl), (Gr2) and (Con) by 

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Tests for the existence of molecular graphs become more involved if we admit var-... 

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