Local Antimagic Chromatic Number for Copies of Graphs

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.