Local Antimagic Chromatic Number for Copies of Graphs

Martin Bača, Andrea Semaničová-Feňovčíková and Tao-Ming Wang
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Martin Bača: Department of Applied Mathematics and Informatics, Technical University, 042 00 Košice, Slovakia
Andrea Semaničová-Feňovčíková: Department of Applied Mathematics and Informatics, Technical University, 042 00 Košice, Slovakia
Tao-Ming Wang: Department of Applied Mathematics, Tunghai University, Taichung 40704, Taiwan

Mathematics, 2021, vol. 9, issue 11, 1-12

Abstract: An edge labeling of a graph G = ( V , E ) using every label from the set { 1 , 2 , ? , | E ( G ) | } exactly once is a local antimagic labeling if the vertex-weights are distinct for every pair of neighboring vertices, where a vertex-weight is the sum of labels of all edges incident with that vertex. Any local antimagic labeling induces a proper vertex coloring of G where the color of a vertex is its vertex-weight. This naturally leads to the concept of a local antimagic chromatic number. The local antimagic chromatic number is defined to be the minimum number of colors taken over all colorings of G induced by local antimagic labelings of G . In this paper, we estimate the bounds of the local antimagic chromatic number for disjoint union of multiple copies of a graph.

Keywords: local antimagic labeling; local antimagic chromatic number; copies of graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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