Are there "binary operations" on graphs like in (https://en.wikipedia.org/wiki/Graph_product), which make the set of all graphs ("under consideration")
- a (abelian) group or
- a (commutative) ring or
- a field or
- some other algebraic structure ? By a graph I mean everything which might be considered a graph, for example a directed graph, undirected graph, graphs with no multiple edges, weighted graphs etc. If so, is there a reference on how the binary operations are construced? I managed to find
but don't have access to it.