几类整循环图的秩的界

Bounds of rank for some integral circulant graphs

循环图是并行计算和分布式计算中一类重要的互联网络拓扑图,整循环图在支持完美状态传递的量子自旋网络模型中具有重要作用。图的秩定义为图的邻接矩阵的秩。利用Ramanujan和,借助Euler函数和Mobius函数,研究了几类整循环图的秩,得到了这些整循环图的秩的较为精确的界。

Circulant graphs are an important class of interconnection networks in parallel and distributed computing,and integral circulant graphs play an important role in modeling quantum spin networks which support the perfect state transfer.The rank of a graph is defined to be the rank of its adjacency matrix.In this note,using Ramanujan sums,by means of the Euler function and the Mobius function,we study the rank for some integral circulant graphs,and deduce the bounds of rank for integral circulant graphs.