On Bridge Graphs with Local Antimagic Chromatic Number 3

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.

Keywords

• local antimagic labeling
• local antimagic chromatic number
• <i>s</i>-bridge graphs