A new class of antimagic join graphs

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 for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K ₂ is antimagic. In this paper, we show that if G ₁ is an m-vertex graph with maximum degree at most 6r+1, and G ₂ is an n-vertex (2r)-regular graph (m?n?3), then the join graph G ₁ ∨ G ₂ is antimagic.