连通图的拉普拉斯特征值之和的下界

A Lower Bound for the Sum of Laplacian Eigenvalues of Connected Graphs

图的拉普拉斯矩阵是指其度对角矩阵和其邻接矩阵之差.设S(G)是图G的前两大的拉普拉斯特征值之和,在所有n阶的连通图中,S(G)的最小值一旦确定,相应的极图也被唯一地刻画.

The Laplacian matrix of a graph is defined to be the difference between the diagonal matrix of vertex degrees and its adjacency matrix.Let S（G） be the sum of the largest two Laplacian eigenvalues of a graph G.Among all connected graphs with n vertices,the unique extremal graph which attains the minimal value of S（G） is determined.