Transfinite diameter on the graph of a polynomial mapping and the DeMarco-Rumely formula

We study Chebyshev constants and transfinite diameter on the graph of a polynomial mapping $f\text{\hspace{0.17em}⁣}:{\mathbb{C}}^2\to {\mathbb{C}}^2$. 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.