Amalg(K_p;K_m,K_n)是反魔幻图

The Amalg(K_p; K_m,K_n) Graph is Antimagic

在1990年,Hartsfield和Ringel提出如下关于图的反魔幻性的猜想:除K_2外,所有连通图都是反魔幻的.猜想一经提出,立即引起了图论学者的极大关注并得到一系列的研究成果.其中,对于Dense graphs、正则图、联图、树、笛卡尔乘积图,已经证明其具有反魔幻性.文章采用构造主对角线为0的分块矩阵的方法,对Amalg(K_p;K_m,K_n)图的反魔幻性进行了深入研究,得出其是反魔幻图的结论.

In 1990,Hartsfield and Ringel conjectured that every connected graph other than K2 is antimagic.The conjecture immediately aroused many researchers＇ attention and a series of results are obtained. Dense graphs,regular graphs,join graphs,trees and the Cartesian product of graphs have been proved to be antimagic.In this paper,a further research on antimagicness of Amalg（Kp; Km,Kn） graph is conducted by constructing a partitioned matrix with the elements in the main diagonal being 0. The results show that the Amalg（Kp; Km,Kn）graph is antimagic.