2023/05/22 by Wai Chee Shiu, Shiu, W. C., Gee-Choon Lau +3
Computer Science · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2305.12933
openalex publication_date 2023/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V, E) be a connected graph. A bijection f: E→ \1, …, |E|\ is called a local antimagic labeling if for any two adjacent vertices x and y, f+(x)≠ f+(y), where f+(x)=∑e∈ E(x)f(e) and E(x) is the set of edges incident to x. Thus a local antimagic labeling induces a proper vertex coloring of G, where the vertex x is assigned the color f+(x). The 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 paper, we present some families of bridge graphs with χla(G)=3 and give several ways to construct bridge graphs with χla(G)=3.