  Presently, models for the parameterization of cross sections for nodal
diffusion nuclear reactor calculations at different conditions using histories
and branches are developed from reactor physics expertise and by trial and
error. In this paper we describe the development and application of a novel
graph theoretic approach (GTA) to develop the expressions for evaluating the
cross sections in a nodal diffusion code. The GTA generalizes existing nodal
cross section models into a ``non-orthogonal'' and extensible dimensional
parameter space. Furthermore, it utilizes a rigorous calculus on graphs to
formulate partial derivatives. The GTA cross section models can be generated in
a number of ways. In our current work we explore a step-wise regression and a
complete Taylor series expansion of the parameterized cross sections to develop
expressions to evaluate them. To establish proof-of-principle of the GTA, we
compare numerical results of GTA generated cross section evaluations with
traditional models for canonical PWR case matrices and the AP1000 lattice
designs.
