  We discuss the extension of the empirical equation: $\left\langle
s_{N}^{2}\right\rangle_{0}\propto g\,l^{2}$, where the subscript 0 denotes the
ideal value with no excluded volume and $g$ the generation number from the root
to the youngest (outermost) generation. By analogy with the linear chain
problem, we introduce the assumption that the scaling relation, $\left\langle
s_{N}^{2}\right\rangle_{0}\propto g^{2\lambda}\,l^{2}$, exists for arbitrary
polymeric architectures, where $\lambda$ is an exponent for the backbone
structure. Then, making use of the relationship between $g$ and $N$ (monomer
number), we can deduce the exponent, $\nu$, for polymers with various
architectures. The theory of the excluded volume effects impose the severe
restriction on the quantities: $\nu_{0}$, $\nu$, and $\lambda$; for instance,
the inequality, $\nu_{0}\ge\frac{1}{d+1}$, must be satisfied for isolated
polymers in good solvents. An intriguing question is whether or not there
exists an actual molecule that violates this inequality. We take up two
examples having $\nu_{0}=1/4$ for $d=2$ and $\nu_{0}=1/6$ for $d=3$, and
discuss this question.
