Recognition of Graphs by Automata

Abstract Graph automata have been introduced by Rosensthiel (1966). He has shown how a graph automaton can study its own structure, by constructing a spanning tree of the underlying graph. Wu and Rosenfeld (1979) have continued the works of Rosensthiel. In particular, they give a linear algorithm permitting a graph automaton to know if its underlying graph has, or has not, a rectangular structure. We give a complete proof of this result. We then generalize this result of the classical structures: torus, cylinder, Moebius band and sphere.