算术结构拉普拉斯矩阵最大特征值的上界

Upper Bound for Maximum Eigenvalue of Laplacian Matrix with Arithmetic Structure

对连通图G算术结构的拉普拉斯矩阵L(G,d)最大特征值λ1(L(G,d))的上界进行了研究,先得到了上界n∑i-1ri,再得到一个更好的上界λ1≤1/2maxi-j(d1+dj+∑k-1,k∞jr k/r1+∑k-i,k∞i rk/rj+∑k-i,k-j|rk/ri-rk/rj|).

An investigation has been made of the upper bound of the maximum eigenvalueλ1(L(G,d))of the n Laplacian matrix L(G,d)of the connected graph G arithmetic structure.First the upper bound n∑i=1ri can be worked out,thus further obtaining a better upper boundλ1≤1/2maxi-j(d1+dj+∑k-1,k∞jr k/r1+∑k-i,k∞i rk/rj+∑k-i,k-j|rk/ri-rk/rj|)