### Abstract

We introduce a new class of graphs called diametral path graphs that properly contains the class of asteroidal triple-free graphs and the class of dominating pair graphs. We characterize the trees as well as the chordal graphs that are diametral path graphs. We present an O(n^{3} m) algorithm deciding whether a given graph has a dominating diametral path. Finally, we study the structure of minimum connected dominating sets in diametral path graphs.

Original language | English (US) |
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Title of host publication | Graph-Theoretic Concepts in Computer Science - 21st International Workshop, WG 1995, Proceedings |

Editors | Manfred Nagl |

Publisher | Springer Verlag |

Pages | 344-357 |

Number of pages | 14 |

ISBN (Print) | 3540606181, 9783540606185 |

State | Published - Jan 1 1995 |

Event | 21st International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1995 - Aachen, Germany Duration: Jun 20 1995 → Jun 22 1995 |

### 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 | 1017 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 21st International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1995 |
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Country | Germany |

City | Aachen |

Period | 6/20/95 → 6/22/95 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Graph-Theoretic Concepts in Computer Science - 21st International Workshop, WG 1995, Proceedings*(pp. 344-357). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1017). Springer Verlag.

**Diametral path graphs.** / Deogun, J. S.; Kratsch, D.

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

*Graph-Theoretic Concepts in Computer Science - 21st International Workshop, WG 1995, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1017, Springer Verlag, pp. 344-357, 21st International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1995, Aachen, Germany, 6/20/95.

}

TY - GEN

T1 - Diametral path graphs

AU - Deogun, J. S.

AU - Kratsch, D.

PY - 1995/1/1

Y1 - 1995/1/1

N2 - We introduce a new class of graphs called diametral path graphs that properly contains the class of asteroidal triple-free graphs and the class of dominating pair graphs. We characterize the trees as well as the chordal graphs that are diametral path graphs. We present an O(n3 m) algorithm deciding whether a given graph has a dominating diametral path. Finally, we study the structure of minimum connected dominating sets in diametral path graphs.

AB - We introduce a new class of graphs called diametral path graphs that properly contains the class of asteroidal triple-free graphs and the class of dominating pair graphs. We characterize the trees as well as the chordal graphs that are diametral path graphs. We present an O(n3 m) algorithm deciding whether a given graph has a dominating diametral path. Finally, we study the structure of minimum connected dominating sets in diametral path graphs.

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UR - http://www.scopus.com/inward/citedby.url?scp=0346309252&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0346309252

SN - 3540606181

SN - 9783540606185

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 344

EP - 357

BT - Graph-Theoretic Concepts in Computer Science - 21st International Workshop, WG 1995, Proceedings

A2 - Nagl, Manfred

PB - Springer Verlag

ER -