  We study Chebyshev constants and transfinite diameter on the graph of a
polynomial mapping $f\colon\mathbb{C}^2\to\mathbb{C}^2$. We show that two
transfinite diameters of a compact subset of the graph (i.e., defined with
respect to two different collections of monomials) are equal when the set has a
certain symmetry. As a consequence, we give a new proof in $\mathbb{C}^2$ of a
pullback formula for transfinite diameter due to DeMarco and Rumely that
involves a homogeneous resultant.
