### Abstract

We consider the question of how much information can be stored by labeling the vertices of a connected undirected graph G using a constant-size set of labels, when isomorphic labelings are not distinguishable. An exact information-theoretic bound is easily obtained by counting the number of isomorphism classes of labelings of G, which we call the information-theoretic capacity of the graph. More interesting is the effective capacity of members of some class of graphs, the number of states distinguishable by a Turing machine that uses the labeled graph itself in place of the usual linear tape. We show that the effective capacity equals the information-theoretic capacity up to constant factors for trees, random graphs with polynomial edge probabilities, and bounded-degree graphs.

Original language | English (US) |
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Title of host publication | Stabilization, Safety, and Security of Distributed Systems - 12th International Symposium, SSS 2010, Proceedings |

Pages | 573-587 |

Number of pages | 15 |

DOIs | |

State | Published - Nov 19 2010 |

Event | 12th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2010 - New York, NY, United States Duration: Sep 20 2010 → Sep 22 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6366 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 12th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2010 |
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Country | United States |

City | New York, NY |

Period | 9/20/10 → 9/22/10 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Stabilization, Safety, and Security of Distributed Systems - 12th International Symposium, SSS 2010, Proceedings*(pp. 573-587). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6366 LNCS). https://doi.org/10.1007/978-3-642-16023-3_44