  We investigate properties of spatial graphs on the standard torus. It is
known that nontrivial embeddings of planar graphs in the torus contain a
nontrivial knot or a nonsplit link due to [1],[2]. Building on this and using
the chirality of torus knots and links [3],[4], we prove that nontrivial
embeddings of simple 3-connected planar graphs in the standard torus are
chiral. For the case that the spatial graph contains a nontrivial knot, the
statement was shown by Castle [5]. We give an alternative proof using minors
instead of the Euler characteristic. To prove the case in which the graph
embedding contains a nonsplit link, we show the chirality of Hopf ladders with
at least three rungs, thus generalising a theorem of Simon [6].
