## Abstract

Let G (V, E) be a simple graph and f be a bijection f: V ∪ E → 1, 2, …, |V|+ |E| where f (|V|) = 1, 2, …, |V|. For a vertex x ∈ V, define its weight w (x) as the sum of labels of all edges incident with x and the vertex label itself. Then f is called a super vertex local antimagic total (SLAT) labeling if for every two adjacent vertices their weights are different. The super vertex local antimagic total chromatic number χ_{slat} (G) is the minimum number of colors taken over all colorings induced by super vertex local antimagic total labelings of G. We classify all trees T that have χ_{slat} (T) = 2, present a class of trees that have χ_{slat} (T) = 3, and show that for any positive integer n ≥ 2 there is a tree T with χ_{slat} (T) = n.

Original language | English (US) |
---|---|

Pages (from-to) | 485-498 |

Number of pages | 14 |

Journal | Electronic Journal of Graph Theory and Applications |

Volume | 9 |

Issue number | 2 |

DOIs | |

State | Published - 2021 |

### Bibliographical note

Funding Information:This research is funded by PUTI 2020 Research Grant, Universitas Indonesia No. NKB-779/UN2.RST/HKP.05.00/2020.

Publisher Copyright:

© 2021

## Keywords

- chromatic number
- super vertex local antimagic total chromatic number
- super vertex local antimagic total labeling
- tree