TY - JOUR
T1 - Chromatic number of super vertex local antimagic total labelings of graphs
AU - Hadiputra, Fawwaz F.
AU - Sugeng, Kiki A.
AU - Silaban, Denny R.
AU - Maryati, Tita K.
AU - Froncek, Dalibor
N1 - Publisher Copyright:
© 2021
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - chromatic number
KW - super vertex local antimagic total chromatic number
KW - super vertex local antimagic total labeling
KW - tree
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U2 - 10.5614/ejgta.2021.9.2.19
DO - 10.5614/ejgta.2021.9.2.19
M3 - Article
AN - SCOPUS:85119527219
SN - 2338-2287
VL - 9
SP - 485
EP - 498
JO - Electronic Journal of Graph Theory and Applications
JF - Electronic Journal of Graph Theory and Applications
IS - 2
ER -