Local Antimagic Vertex Coloring of a Graph

Abstract:

Let G= (V, E) be a connected graph with | V| = n and | E| = m. A bijection f: E→ { 1 , 2 , ⋯ , m} is called a local antimagic labeling if for any two adjacent vertices u and v, w(u) ≠ w(v) , where w(u) = ∑ e∈E(u)f(e) , and E(u) is the set of edges incident to u. Thus any local antimagic labeling induces a proper vertex coloring of G where the vertex v is assigned the color w(v). 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 several basic results on this new parameter.

Año de publicación:

2017

Keywords:

• Antimagic labeling
• Local antimagic chromatic number
• Local antimagic labeling

Fuente:

scopus