摘要
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 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.
基金
Supported by Fundamental Research Funds for the Central Universities(Grant No.2011B019)
National Natural Science Foundation of China(Grant Nos.11101020,11171026,10201022and10971144)
Natural Science Foundation of Beijing(Grant No.1102015)
