  We provide a string theory embedding for N = 1 superconformal field theories
defined by bipartite graphs inscribed on a disk. We realize these theories by
exploiting the close connection with related N = 2 generalized (A_(k-1),
A_(n-1)) Argyres-Douglas theories. The N = 1 theory is obtained from spacetime
filling D5-branes wrapped on an algebraic curve and NS5-branes wrapped on
special Lagrangians of C^2 which intersect along the BPS flow lines of the
corresponding N = 2 Argyres-Douglas theory. Dualities of the N = 1 field theory
follow from geometric deformations of the brane configuration which leave the
UV boundary conditions fixed. In particular we show how to recover the
classification of IR fixed points from cells of the totally non-negative
Grassmannian Gr^(tnn)_(k,n+k). Additionally, we present evidence that in the 3D
theory obtained from dimensional reduction on a circle, VEVs of line operators
given by D3-branes wrapped over faces of the bipartite graph specify a
coordinate system for Gr^(tnn)_(k,n+k).
