Lexicographic product graphs P m [ P n ] are antimagic

Abstract

A graph with q edges is called a n t i m a g i c if its edges can be labeled with 1, 2, …, q such that the sums of the labels on the edges incident to each vertex are distinct. Hartsfield and Ringel conjectured that every connected graph other than K 2 is antimagic. In this paper, through a labeling method and a modification on this labeling, we obtained that the lexicographic product graphs P m [ P n ] are antimagic. Keywords: Antimagic graph, Lexicographic product, Path