## Abstract

A set of vertices S in a graph G is independent if no neighbor of a vertex of S belongs to S. A set of vertices U in a graph G is irredundant if each vertex v of U has a private neighbor, which may be v itself, i.e., a neighbor of v which is not a neighbor of any other vertex of U. The independence number α (resp. upper irredundance number I R) is the maximum number of vertices of an independent (resp. irredundant) set of G. In previous work, a series of best possible lower and upper bounds on α and some other usual invariants of G were obtained by the system AGX 2, and proved either automatically or by hand. These results are strengthened in the present paper by systematically replacing α by I R. The resulting conjectures were tested by AGX which could find no counter-example to an upper bound nor any case where a lower bound could not be shown to remain tight. Some proofs for the bounds on α carry over. In all other cases, new proofs are provided.

Original language | English |
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Pages (from-to) | 3497-3510 |

Number of pages | 14 |

Journal | Discrete Applied Mathematics |

Volume | 157 |

Issue number | 17 |

DOIs | |

Publication status | Published - Oct 28 2009 |

Externally published | Yes |

## Keywords

- AGX
- Extremal graph
- Invariant
- Upper irredundance

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics