On bridge graphs with local antimagic chromatic number 3

This is the authors' abstract. We don't add key points for this paper.

Abstract 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. 2010 AMS Subject Classifications: 05C78, 05C69.