Hey everyone. I found the following papers and lecture that pertain to flat graph algebras. Hope you find them as useful as I did.
Dejan Delić “Finite Bases for Flat Graph Algebras” Journal of Algebra 2002
William A Lampe “Full duality among graph algebras and flat graph algebras” 1991
A lecture on combinatorial optimization: http://www.cs.illinois.edu/class/sp10/cs598csc/Lectures/Lecture14.pdf