Algebraic structures on graphs

In this paper we consider directed graphs with algebraic structures: group-graphs, ringgraphs, involutorial graphs, affine graphs, graphs of morphisms between graphs, graphs of reduced paths of an involutorial graph, etc. We show also how several well-known algebraic constructions can be carried over to graphs. As a typical example we generalize the construction of the group of automorphisms of a set, by constructing a group-graph associated with any given graphΓ. It is the group-graph of reduced paths of the involutorial graph associated to the graph of automorphisms ofΓ.