A computable graph is computably categorical if any two computable presentations of the graph are computably isomorphic. In this paper we investigate the class of computably categorical graphs. We restrict ourselves to strongly locally finite graphs; these are the graphs all of whose components are finite. We present a necessary and sufficient condition for certain classes of strongly locally finite graphs to be computably categorical. We prove that if there exists an infinite -set of components that can be properly embedded into infinitely many components of the graph then the graph is not computably categorical. We outline the construction of a strongly locally finite computably categorical graph with an infinite chain of properly embedded components. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Csima, B. F., Khoussainov, B., & Liu, J. (2008). Computable categoricity of graphs with finite components. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5028 LNCS, pp. 139–148). https://doi.org/10.1007/978-3-540-69407-6_15
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