TY - GEN

T1 - Local Antimagic Vertex Coloring of Corona Product Graphs Pn ∘ Pk

AU - Sugeng, Kiki Ariyanti

AU - Setiawan,

N1 - This research has supported by PUTI KI-Universitas Indonesia 2020 Research Grant No. NKB779/UN2.RST/HKP.05.00/ 2020.

PY - 2022/2/8

Y1 - 2022/2/8

N2 - 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 G ∘ H 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 (Pn ∘ Pk) for the corona product of path Pn and Pk where k is a small number.

AB - 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 G ∘ H 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 (Pn ∘ Pk) for the corona product of path Pn and Pk where k is a small number.

KW - Antimagic labeling

KW - Local antimagic labeling

KW - Local antimagic chromatic number

KW - Corona product graph

KW - Path

U2 - 10.2991/acsr.k.220202.014

DO - 10.2991/acsr.k.220202.014

M3 - Conference contribution

SN - 978-94-6239-529-9

T3 - Advances in Computer Science Research

SP - 65

EP - 70

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

PB - Atlantis Press International

T2 - International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)

Y2 - 27 November 2021 through 27 November 2021

ER -