图Kn-Cn-1的沙堆群

The sandpile group of Kn-Cn-1

一个连通图的沙堆群,又称临界群或雅可比群,是一个有限的阿贝尔群,其阶数为图中生成树的数目.本文用代数方法确定了Kn-Cn-1的沙堆群的结构,Kn-Cn-1表示从完全图Kn中删掉圈Cn-1上的n-1条边所得到的图.

The sandpile group of a connected graph,also known as critical group,or Jacobian group,is a finite Abelian group,whose order is the number of spanning trees in the graph.In this paper,using the algebraic method,we completely determine the structure of the sandpile group of Kn-Cn-1,where Kn-Cn-1 denotes the graph obtained by removing from the complete graph Kn the n-1 edges of a cycle Cn-1.