Graph Operations and Free Graph Algebras

We introduce a concept of graph algebra that generalizes the traditional concept of algebra in the sense that (1) we use graphs rather than sets as carriers, and (2) we generalize algebraic operations to diagrammatic operations over graphs, which we call graph operations.Our main objective is to extend the construction of term algebras, i.e., free algebras, for the new setting. The key mechanism for the construction of free graph algebras are …