Graph language recognizability is defined and investigated by virtue of the syntactic magmoid, analogously with the syntactic monoid of a word language. In this setup, the syntax complexity of a given recognizable graph language can be determined, giving rise to a syntactic classification inside the class of recognizable graph languages.
Automata operating on general graphs have been introduced by virtue of graphoids. In this paper we construct a graph automaton that recognizes k-colorable graphs.
A new class of hypergroupoids, deriving from binary relations, is presented, via the introduced path hyperoperation. Its properties are investigated and its connections with Graph Theory are also delineated. Moreover, we present an application of this hyperoperation to assembly line designing and management.