## Abstract

In this paper, we continue the study of the L-Grundy domination number of a graph introduced and first studied in [Grundy dominating sequences and zero forcing sets, Discrete Optim. 26 (2017) 66-77]. A vertex in a graph dominates itself and all vertices adjacent to it, while a vertex totally dominates another vertex if they are adjacent. A sequence of distinct vertices in a graph G is called an L-sequence if every vertex v in the sequence is such that v dominates at least one vertex that is not totally dominated by any vertex that precedes v in the sequence. The maximum length of such a sequence is called the L-Grundy domination number, γ^{L} _{gr}(G), of G. We show that the L-Grundy domination number of every forest G on n vertices equals n, and we provide a linear-time algorithm to find an L-sequence of length n in G. We prove that the decision problem to determine if the L-Grundy domination number of a split graph G is at least k for a given integer k is NP-complete. We establish a lower bound on γ^{L} _{gr}(G) when G is a regular graph, and investigate graphs G on n vertices for which γ^{L} _{gr}(G) = n.

Original language | English |
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Pages (from-to) | 3205-3215 |

Number of pages | 11 |

Journal | Filomat |

Volume | 34 |

Issue number | 10 |

DOIs | |

Publication status | Published - Dec 2020 |

## Keywords

- Forests
- Grundy total domination number
- L-grundy domination number
- Regular graphs
- Split graphs

## ASJC Scopus subject areas

- General Mathematics