## Abstract

For a graph G = (V, E), a set S ⊆ V is total irredundant if for every vertex v ∈ V, the set N[v] - N[S - {v}] is not empty. The total irredundance number ir_{t}(G) is the minimum cardinality of a maximal total irredundant set of G. We study the structure of the class of graphs which do not have any total irredundant sets; these are called ir_{t}(0)-graphs. Particular attention is given to the subclass of ir_{t}(0)-graphs whose total irredundance number either does not change (stable) or always changes (unstable) under arbitrary single edge additions. Also studied are ir_{t}(0)-graphs which are either stable or unstable under arbitrary single edge deletions.

Original language | English |
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Pages (from-to) | 33-46 |

Number of pages | 14 |

Journal | Ars Combinatoria |

Volume | 61 |

Publication status | Published - 2001 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics