On Bridge Graphs with Local Antimagic Chromatic Number 3 - Wai-Chee Shiu; Gee-Choon Lau; Ruixue Zhang (Mathematics)
Let <semantics>G=(V,E)</semantics> be a connected graph. A bijection <semantics>f:E→{1,…,|E|}</semantics> is called a local antimagic labeling if, for any two adjacent vertices x and y, <semantics>f+(x)≠f+(y)</semantics>, where <semantics>f+(x)=∑e∈E(x)f(e)</semantics>, and <semantics>E(x)</semantics> 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 <semantics>f+(x)</semantics>. The local antimagic chromatic number <semantics>χla(G)</semantics> 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 <semantics>χla(G)=3</semantics> and give several ways to construct bridge graphs with <semantics>χla(G)=3</semantics>.