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 G1 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 G1 V G2 is antimagic.
A labeling of a graph G is a bijection from E（G） to the set {1,2,…,｜E （G）｜ }.A labeling 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.We say that a graph is antimagic if it has an antimagic labeling.Hartsfield and Ringel conjectured in 1990 that every graph other than 2 K is antimagic.In this paper,we show that the antimagic conjecture is false for the case of disconnected graphs.Furthermore,we find some classes of disconnected graphs that are antimagic and some classes of graphs whose complement are disconnected are antimagic.
A labelingfof 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 anfwhich is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K2 is antimagic. In this paper, we show that if G1 is an m-vertex graph with maximum degree at most 6r＋ 1, and G2 is an n-vertex （2r）-regular graph （m≥n≥3）, then the join graph G1 v G2 is antimagic.
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 2K is antimagic. In this paper, we show that some graphs with even factors are antimagic, which generalizes some known results.
