### Abstract

Summary form only given, as follows. Graph entropy is an information-theoretic functional on a graph and a probability distribution on its vertex set. Fixing the probability distribution, it is subadditive with respect to graph union. This property has been used by several authors to derive nonexistence bounds in graph covering problems. Here the authors deal with the conditions for additivity instead of subadditivity. For two complementary graphs it was proved by Csiszar et al. that additivity for every possible probability distribution is equivalent to the perfectness of the involved graph(s). Necessary and sufficient conditions of additivity (for every probability distribution) are given in full generality. This can be considered as a generalization of the concept of perfect graphs, giving some insight into the kind of graph properties to which graph entropy is sensitive.

Original language | English |
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Title of host publication | 1990 IEEE Int Symp Inf Theor |

Publisher | Publ by IEEE |

Pages | 171 |

Number of pages | 1 |

Publication status | Published - 1990 |

Event | 1990 IEEE International Symposium on Information Theory - San Diego, CA, USA Duration: Jan 14 1990 → Jan 19 1990 |

### Other

Other | 1990 IEEE International Symposium on Information Theory |
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City | San Diego, CA, USA |

Period | 1/14/90 → 1/19/90 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*1990 IEEE Int Symp Inf Theor*(pp. 171). Publ by IEEE.

**When is graph entropy additive? Or : Perfect couples of graphs.** / Korner, Janos; Simonyi, Gabor; Tuza, Z.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*1990 IEEE Int Symp Inf Theor.*Publ by IEEE, pp. 171, 1990 IEEE International Symposium on Information Theory, San Diego, CA, USA, 1/14/90.

}

TY - GEN

T1 - When is graph entropy additive? Or

T2 - Perfect couples of graphs

AU - Korner, Janos

AU - Simonyi, Gabor

AU - Tuza, Z.

PY - 1990

Y1 - 1990

N2 - Summary form only given, as follows. Graph entropy is an information-theoretic functional on a graph and a probability distribution on its vertex set. Fixing the probability distribution, it is subadditive with respect to graph union. This property has been used by several authors to derive nonexistence bounds in graph covering problems. Here the authors deal with the conditions for additivity instead of subadditivity. For two complementary graphs it was proved by Csiszar et al. that additivity for every possible probability distribution is equivalent to the perfectness of the involved graph(s). Necessary and sufficient conditions of additivity (for every probability distribution) are given in full generality. This can be considered as a generalization of the concept of perfect graphs, giving some insight into the kind of graph properties to which graph entropy is sensitive.

AB - Summary form only given, as follows. Graph entropy is an information-theoretic functional on a graph and a probability distribution on its vertex set. Fixing the probability distribution, it is subadditive with respect to graph union. This property has been used by several authors to derive nonexistence bounds in graph covering problems. Here the authors deal with the conditions for additivity instead of subadditivity. For two complementary graphs it was proved by Csiszar et al. that additivity for every possible probability distribution is equivalent to the perfectness of the involved graph(s). Necessary and sufficient conditions of additivity (for every probability distribution) are given in full generality. This can be considered as a generalization of the concept of perfect graphs, giving some insight into the kind of graph properties to which graph entropy is sensitive.

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M3 - Conference contribution

SP - 171

BT - 1990 IEEE Int Symp Inf Theor

PB - Publ by IEEE

ER -