Lexicographic product graphs are antimagic

Abstract

A graph with edges is called if its edges can be labeled with 1, 2, , 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 is antimagic. In this paper, through a labeling method and a modification on this labeling, we obtained that the lexicographic product graphs are antimagic.

Keywords

• antimagic graph
• lexicographic product
• path