LOCAL ANTIMAGIC COLORING OF SOME GRAPHS
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Date
2023
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arXiv preprint arXiv:2306.03559
Abstract
Consider a simple graph G without K2 component with vertex set V and edge set E. Local antimagic labeling f of G is a one-to-one mapping of edges to distinct positive integers 1, 2, . . . , |E| such that the weights of adjacent vertices are distinct, where the weight of a vertex is the sum of labels assigned to the edges incident to it. These weights of the vertex induced by local antimagic labeling result in a proper vertex coloring of the graph G. We define the local antimagic chromatic number of G, denoted as χla(G), as the smallest number of distinct weights obtained across all possible local antimagic labelings of G. In this paper, we explore the local antimagic chromatic numbers of various classes of graphs, including the union of certain graph families, the corona product of graphs, and the necklace graph. Additionally, we provide constructions for infinitely many graphs for which χla(G) equals the chromatic number χ(G) of the graph