Local Antimagic Vertex Coloring of Corona Product Graphs P_n ∘ P_k

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) = Σ_{e ∈ 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 i^th vertex of G adjacent to every vertex of the i^th copy of H, where 1 ≤ i ≤ |V(G)|. The local antimagic chromatic number, denoted χ_la (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 χ_la (P_n ∘ P_k) for the corona product of path P_n and P_k where k is a small number.

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  - 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  -