Antimagic Labeling of the Lexicographic Product Graph Km,n[Pk]

A labeling f of a graph G is a bijection from its edge set E ( G ) to the set { 1 , 2 , … , | E ( G ) | } , which is antimagic if the vertex-sums are pairwise distinct, where the vertex-sum at one vertex is the sum of labels of all edges incident to such vertex. A graph is called antimagic if it admits an antimagic labeling f . In this paper, we show that the graph K m , n [ P k ] , which is the lexicographic product of the complete bipartite graph K m , n and path P k , is antimagic.