Local Antimagic Vertex Coloring of Corona Product Graphs Pn ∘ Pk

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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) = 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.
Original languageEnglish
Title of host publicationProceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
PublisherAtlantis Press International
Pages65-70
ISBN (Print)978-94-6239-529-9
DOIs
Publication statusPublished - 8 Feb 2022
EventInternational Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021) - Jember, Indonesia
Duration: 27 Nov 202127 Nov 2021

Publication series

NameAdvances in Computer Science Research
PublisherAtlantis Press International B.V.
ISSN (Print)2352-538X

Conference

ConferenceInternational Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
Period27/11/2127/11/21

Keywords

  • Antimagic labeling
  • Local antimagic labeling
  • Local antimagic chromatic number
  • Corona product graph
  • Path

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