2018/08/15 by S. Arumugam, Arumugam, S., Yi-Chun Lee +5
Computer Science · #05C15 #05C78 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.1808.04956
openalex publication_date 2018/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G = (V, E) be a finite simple undirected graph without K2 components. A bijection f : E → \1, 2,⋯, |E|\ is called a \bf 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) = ∑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). The \bf local antimagic chromatic number χla(G) is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. In this article among others we determine completely the local antimagic chromatic number χla(G∘ Km) for the corona product of a graph G with the null graph Km on m≥ 1 vertices, when G is a path Pn, a cycle Cn, and a complete graph Kn.