  Two isomorphic graphs can have inequivalent spatial embeddings in 3-space. In
this way, an isomorphism class of graphs contains many spatial graph types. A
common way to measure the complexity of a spatial graph type is to count the
minimum number of straight sticks needed for its construction in 3-space. In
this paper, we give estimates of this quantity by enumerating stick diagrams in
a plane. In particular, we compute the planar stick indices of knotted graphs
with low crossing numbers. We also show that if a bouquet graph or a
theta-curve has the property that its proper subgraphs are all trivial, then
the planar stick index must be at least seven.
