  We study three resistance distance-based graph invariants: the Kirchhoff
index, and two modifications, namely, the multiplicative degree-Kirchhoff index
and the additive degree-Kirchhoff index. In work in press, one of the present
authors (2014) and Sun et al. (2014) independently obtained (different)
formulas for the Kirchhoff index of subdivisions of graphs. Huang et al. (2014)
obtained a formula for the Kirchhoff index of triangulations of graphs. In our
paper, first we derive formulae for the additive degree-Kirchhoff index and the
multiplicative degree-Kirchhoff index of subdivisions and triangulations, as
well as a new formula for the Kirchhoff index of triangulations, in terms of
invariants of $G$. Then comparisons are made between each of our Kirchhoffian
graph invariants for subdivision and triangulation. Finally, formulae for these
graph invariants of iterated subdivisions and triangulations of graphs are
obtained.
