Upper and Lower Bounds for Some Invariants

Assume that an invariant x for single coronoids is selected. Then it is of interest to determine the upper and lower bounds of x, if they exist, in terms of an other invariant, say y. Such an analysis may result in inequalities of the kind f y) x g(y), where f(y) = and y(y) = iinctions to be determined. 

The functions ( j)jnax( ) special cases, which were encountered in eqn. 

2 Functions of the Number of Hexagons and of the Number of Internal Vertices 

The inequalities for n and h in terms of h and n, respectively, as given in eqns. (3.57) and (3.60), were specialized for single coronoids by inserting = 1. The results are found among the relations of Table 3. All the other inequalities in this table were easily deduced from the two mentioned relations and those of Table 1. Some of the inequalities in terms of A, viz. those for n, m, n and n, are given in Vol. I—3.2.3. 

All the upper and lower bounds under consideration (when they exist) are realized in 

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