Universal Labeling Algebras as Invariants of Layered Graphs

In this work we will study the universal labeling algebra A(Gamma), a related algebra B(Gamma), and their behavior as invariants of layered graphs. We will introduce the notion of an upper vertex-like basis, which allows us to recover structural information about the graph Gamma from the algebra B(Gamma). We will use these bases to show that several classes of layered graphs are uniquely identified by their corresponding algebras B(Gamma).