Graph operations and categorical constructions

Abstract

Most of the usual binary graph operations from disjoint union up to the complete product are interpreted categorically, using the categories Gra, CGra and EGra. This way it is proved that these categories have coproducts, products and tensor products. As a consequence, it turns out that the respective categories with strong morphisms SGra and SEGra do not admit any of these categorical constructions. It is shown that the functors derived from the respective tensor products and products in Gra, CGra and EGra have right adjoints.