On Bridge Graphs with Local Antimagic Chromatic Number 3

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 χ l a ( 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 χ l a ( G ) = 3 and give several ways to construct bridge graphs with χ l a ( G ) = 3 .