  The properties of ideal tri-functional dendrimers with forty-five,
ninety-three and one hundred and eighty-nine branches are investigated. Three
methods are employed to calculate the mean-square radius of gyration,
$g$-ratios, asphericity, shape parameters and form factor. These methods
include a Kirchhoff matrix eigenvalue technique, the graph theory approach of
Benhamou et al. (2004), and Monte Carlo simulations using a growth algorithm. A
novel technique for counting paths in the graph representation of the
dendrimers is presented. All the methods are in excellent agreement with each
other and with available theoretical predictions. Dendrimers become more
symmetrical as the generation and the number of branches increase.
