Local Antimagic Vertex Coloring of Wheel Graph and Helm Graph

F. F. Hadiputra, D. R. Silaban, T. K. Maryati

2019

Abstract

Let 𝜒(𝐺) be a chromatic number of vertex coloring of a graph G. A bijection 𝑓:𝐸→{1,2,3,…,|𝐸(𝐺)|} is called local antimagic vertex coloring if for any adjacent vertices do not share the same weight, where the weight of a vertex in 𝐺 is the sum of the label of edges incident to it. We denote the minimum number of distinct weight of vertices in 𝐺 so that the graph 𝐺 admits a local antimagic vertex coloring as 𝜒𝑙𝑎(𝐺). In this study, we established the missing value of 𝜒𝑙𝑎 for a case in wheel graph and 𝜒𝑙𝑎 for helm graph.

Paper Citation

in Harvard Style

Hadiputra F., Silaban D. and Maryati T. (2019). Local Antimagic Vertex Coloring of Wheel Graph and Helm Graph. In Proceedings of the 1st International MIPAnet Conference on Science and Mathematics - Volume 1: IMC-SciMath, ISBN 978-989-758-556-2, pages 185-189. DOI: 10.5220/0010138400002775

in Bibtex Style

@conference{imc-scimath19,
author={F. F. Hadiputra and D. R. Silaban and T. K. Maryati},
title={Local Antimagic Vertex Coloring of Wheel Graph and Helm Graph},
booktitle={Proceedings of the 1st International MIPAnet Conference on Science and Mathematics - Volume 1: IMC-SciMath,},
year={2019},
pages={185-189},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010138400002775},
isbn={978-989-758-556-2},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 1st International MIPAnet Conference on Science and Mathematics - Volume 1: IMC-SciMath,
TI - Local Antimagic Vertex Coloring of Wheel Graph and Helm Graph
SN - 978-989-758-556-2
AU - Hadiputra F.
AU - Silaban D.
AU - Maryati T.
PY - 2019
SP - 185
EP - 189
DO - 10.5220/0010138400002775