关于煎饼网络及层次环煎饼网络的几个猜想

Some Conjectures About the Pancake Networks and the Hierarchical Ring of Pancake Networks

煎饼网络是由互连网络的群论模型设计出来的一类典型的超级计算机互连网络。关于煎饼网络师海忠提出了一个猜想-猜想1,但煎饼网络有一个弱点即结点度随着规模的增大而迅速增大,为了改进这一缺点师海忠提出了互连网络的层次环群论模型。在这篇文章中,首先,汪生龙给出了煎饼网络当n=5时的两种圈分解,其次师海忠提出了关于该网络的一个猜想-猜想2,当Cayley图层次环网络中的Cayley图取煎饼网络时得到煎饼层次环网络的猜想-猜想2/。

Pancake networks designed by the group theory model of the interconnection network is a kind of typical super computer network. Hai-Zhong Shi proposed a conjecture （conjecture1） about pancake graph but pan-cake network has a weakness that node degree increases quickly with the increase of the size. In order to improve this defect, interconnection network hierarchical ring group theory model is proposed by Hai-Zhong Shi. In this pa-per, at first Sheng-Long Wang give two class decomposition of circle of pancake network when n=5. the second Hai-Zhong Shi proposed a conjecture （conjecture2） on the network, when Cayley is the pancake graph conjecture2 changed conjecture2 about pancake hierarchical ring network. Furthermore, Sheng-Long Wang prove that the con-jecture is correct in the situation of low dimension.