A 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 K2 is antimagic. In this paper, we show that if G ₁ is an n-vertex graph with minimum degree at least r, and G2 is an m-vertex graph with maximum degree at most 2r ? 1 (m ≥ n), then G ₁ ? G ₂ is antimagic.