Local Antimagic Vertex Coloring of Gear Graph

DOI

10.2991/acsr.k.220202.015How to use a DOI?

Keywords

Antimagic labeling; Local antimagic labeling; Local antimagic chromatic number; Gear graph

Abstract

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 χ_la (G). This paper contribution is to determine the local antimagic chromatic number χ_la (G_n) 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 W_n. The gear graph G_n has 2n+1 vertices and 3n edges.

Copyright

© 2022 The Authors. Published by Atlantis Press International B.V.

Open Access

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

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TY  - CONF
AU  - Masdaria Natalina Br Silitonga
AU  - Kiki Ariyanti Sugeng
PY  - 2022
DA  - 2022/02/08
TI  - Local Antimagic Vertex Coloring of Gear Graph
BT  - Proceedings of the  International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
PB  - Atlantis Press
SP  - 71
EP  - 75
SN  - 2352-538X
UR  - https://doi.org/10.2991/acsr.k.220202.015
DO  - 10.2991/acsr.k.220202.015
ID  - Silitonga2022
ER  -