A Class of Antimagic Join Graphs  

作　　者：Tao WANG Ming Ju LIU De Ming LI 

机构地区：[1]Department of Foundation, North China Institute of Science and Technology [2]LMIB and Department of Mathematics, Beihang University [3]Department of Mathematics, Capital Normal University

出　　处：《Acta Mathematica Sinica,English Series》2013年第5期1019-1026,共8页数学学报（英文版）

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)

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.

关 键 词：Antimagic LABELING join graphs 

分 类 号：O157.5[理学—数学] TS952.83[理学—基础数学]