Generation of Anti-Magic Graphs

An anti-magic labeling of a graph G is a one-to-one correspondence between E(G) and {1, 2, · · ·, |E|} such that the vertex-sum for distinct vertices are different. Vertex-sum of a vertex u ∈ V(G) is the sum of labels assigned to edges incident to the vertex u. In this paper, we prove that the splittance of an anti-magic graph admits anti-magic labeling. It was conjectured by Hartsfield and Ringel that every tree other than K2 has an anti-magic labeling. In this paper, we prove that there exists infinitely many trees that are anti-magic.