The 1/Nc expansion is one of the very few methods we have for generating a
systematic expansion of QCD at the energy scale relevant to hadron structure.
The present formulation of this theory relies on the double-line notation for
calculating the leading order of a diagram in the 1/Nc expansion, where the
local SU(Nc) gauge symmetry is substituted by a U(Nc) symmetry and the
associated U(1) ghost field is ignored. In the current work we demonstrate the
insufficiency of this formulation for describing certain non-planar diagrams.
We derive a more complete set of Feynman rules that include the U(1) ghost
field and provide a useful tool for calculating both color factors and 1/Nc
orders of all color-singlet diagrams