TY - GEN

T1 - Local Antimagic Vertex Coloring of Gear Graph

AU - Silitonga, Masdaria Natalina Br

AU - Sugeng, Kiki Ariyanti

PY - 2022/2/8

Y1 - 2022/2/8

N2 - Let G = (V, E) be a graph that consist of a vertex set V and an edge set E. The local antimagic labeling f of a graph G with edge-set E is a bijection map from E to {1, 2, …, |E|} such that w(u) ≠ w(v), where w(u) = ∑e ∈ E(u) f(e) and E(u) is the set of edges incident to u. In this labeling, every vertex v is assigned w(v) as its color. The minimum number of colors in a local antimagic labelling, is called a local antimagic chromatic number and denoted by χla (G). This paper contribution is to determine the local antimagic chromatic number χla (Gn) of a gear graph. A gear graph is a graph obtained by inserting additional vertex between each pair of adjacent vertices on the circumference of the wheel graph Wn. The gear graph Gn has 2n+1 vertices and 3n edges.

AB - Let G = (V, E) be a graph that consist of a vertex set V and an edge set E. The local antimagic labeling f of a graph G with edge-set E is a bijection map from E to {1, 2, …, |E|} such that w(u) ≠ w(v), where w(u) = ∑e ∈ E(u) f(e) and E(u) is the set of edges incident to u. In this labeling, every vertex v is assigned w(v) as its color. The minimum number of colors in a local antimagic labelling, is called a local antimagic chromatic number and denoted by χla (G). This paper contribution is to determine the local antimagic chromatic number χla (Gn) of a gear graph. A gear graph is a graph obtained by inserting additional vertex between each pair of adjacent vertices on the circumference of the wheel graph Wn. The gear graph Gn has 2n+1 vertices and 3n edges.

KW - Antimagic labeling

KW - Local antimagic labeling

KW - Local antimagic chromatic number

KW - Gear graph

U2 - 10.2991/acsr.k.220202.015

DO - 10.2991/acsr.k.220202.015

M3 - Conference contribution

SN - 978-94-6239-529-9

T3 - Advances in Computer Science Research

SP - 71

EP - 75

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 -