中文摘要：

设G是n阶简单连通无向图,其中n≥5.证明了图G的Laplacian矩阵的第三个不变因子S3（G）≤n.刻画了满足S3（G）=n,n-1,n-2,n-3的所有简单连通无向图.

英文摘要：

Let G be a simple connected graph with n≥5 vertices.It was proved that s3（G）≤n,and the graphs which satisfy that s3（G）=n,n-1,n-2,or n-3 were characterized,where s3（G） is the third invariant factor of the Laplacian matrix of G.