Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)

# Local Antimagic Vertex Coloring of Corona Product Graphs Pn ∘ Pk

Authors
Setiawan, Kiki Ariyanti Sugeng*
Department of Mathematics, Faculty of Mathematics and Sciences, Universitas Indonesia, Depok 16424, Indonesia
*Corresponding author. Email: kiki@sci.ui.ac.id
Corresponding Author
Kiki Ariyanti Sugeng
Available Online 8 February 2022.
DOI
10.2991/acsr.k.220202.014How to use a DOI?
Keywords
Antimagic labeling; Local antimagic labeling; Local antimagic chromatic number; Corona product graph; Path
Abstract

Let G = (V, E) be a graph with vertex set V and edge set E. A bijection map f : E → {1,2, …, |E|} is called a local antimagic labeling if, for any two adjacent vertices u and v, they have different vertex sums, i.e. w(u) ≠ w(v), where the vertex sum w(u) = Σe E(u) f(e), and E(u) is the set of edges incident to u. Thus, any local antimagic labeling induces a proper vertex coloring of G where the vertex v is assigned the color (vertex sum) w(v). Let G and H be two graphs. The Corona product GH is obtained by taking one copy of G along with |V(G)| copies of H, and via putting extra edges making the ith vertex of G adjacent to every vertex of the ith copy of H, where 1 ≤ i ≤ |V(G)|. The local antimagic chromatic number, denoted χla (G), is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. In this paper, we present the local antimagic chromatic number χla (PnPk) for the corona product of path Pn and Pk where k is a small number.

Open Access
This is an open access article under the CC BY-NC license.

Volume Title
Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
Series
Publication Date
8 February 2022
ISBN
978-94-6239-529-9
ISSN
2352-538X
DOI
10.2991/acsr.k.220202.014How to use a DOI?
Open Access
This is an open access article under the CC BY-NC license.

TY  - CONF
AU  - Setiawan
AU  - Kiki Ariyanti Sugeng
PY  - 2022
DA  - 2022/02/08
TI  - Local Antimagic Vertex Coloring of Corona Product Graphs Pn ∘ Pk
BT  - Proceedings of the  International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
PB  - Atlantis Press
SP  - 65
EP  - 70
SN  - 2352-538X
UR  - https://doi.org/10.2991/acsr.k.220202.014
DO  - 10.2991/acsr.k.220202.014
ID  - 2022
ER  -