Chromatic number of super vertex local antimagic total labelings of graphs

Fawwaz F. Hadiputra, Kiki A. Sugeng, Denny R. Silaban, Tita K. Maryati, Dalibor Froncek

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 χslat (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 χslat (T) = 2, present a class of trees that have χslat (T) = 3, and show that for any positive integer n ≥ 2 there is a tree T with χslat (T) = n.

Original languageEnglish (US)
Pages (from-to)485-498
Number of pages14
JournalElectronic Journal of Graph Theory and Applications
Volume9
Issue number2
DOIs
StatePublished - 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

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