## Abstract

Let G=(V,E) be a graph. A set S⊆V is a total restrained dominating set if every vertex is adjacent to a vertex in S, and every vertex in V−S is adjacent to a vertex in V−S. The total restrained domination number of G, denoted γ_{tr}(G), is the smallest cardinality of a total restrained dominating set of G. In this paper we show that if G is a K_{1,ℓ}-free graph with δ≥ℓ≥3 and δ≥5, then γ_{tr}(G)≤n1−[Formula presented]+o_{δ}(1).

Original language | English |
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Pages (from-to) | 429-439 |

Number of pages | 11 |

Journal | Discrete Applied Mathematics |

Volume | 357 |

DOIs | |

Publication status | Published - 15 Nov 2024 |

## Keywords

- Domination
- Graph
- Total restrained domination
- Upper bound

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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