Cellular graph automata. II. graph and subgraph isomorphism, graph structure recognition

Abstract

This paper deals with cellular automata in which the intercell connections define a graph of bounded degree. It discusses acceptance tasks that involve the detection of graph or subgraph isomorphism in time proportional to the diameter of the given graph. In some of the algorithms, special assumptions are made about the “homogeneity” of the graph; these assumptions hold for many important classes of graphs, including trees and arrays. The paper also examines types of graph structures that can be recognized by these automata. Diameter-time algorithms are presented for the recognition of cycles, strings, trees, cliques, rectangular and square arrays, Eulerian graphs, bipartite and complete bipartite graphs, stars, and wheels. The recognition of planar graphs is also discussed.