Lexicographic product graphs P m [ P n ] are antimagic

摘要

A graph withqedges is calledantimagicif its edges can be labeled with 1, 2,…,qsuch that the sums of the labels on the edges incident to each vertex are distinct. Hartsfield and Ringel conjectured that every connected graph other thanK2is antimagic. In this paper, through a labeling method and a modification on this labeling, we obtained that the lexicographic product graphsPm[Pn]are antimagic.