有向图的无符号拉普拉斯谱半径的新上下界

Some New Upper and Lower Boundon the Spectral Radius of the Signless Laplacian Matrix of a Digraph

设G是一个n阶的简单有向连通图,令A(G)为有向图G的邻接矩阵,D(G)为有向图G的出度对角矩阵,则有向图G的无符号拉普拉斯矩阵可以表示为Q(G)=A(G)+D(G).利用图中顶点v_i的出度d_i^+和平均二次出度m_i^+,给出一些有向图G的无符号拉普拉斯矩阵谱半径q_1(G)更精细化的上下界,并通过数值例子证实新上下界的有效性.

Let G be a simple connected digraph,A（ G） denote its adjacency matrix,and D（ G） denote the diagonal matrix of its vertex out degrees,then the signless Laplacian matrix of G is Q（G） = A（ G） ＋D（ G）. In this paper,we obtain some new upper and lower bound on the spectral radius q1（ G） of the signless Laplacian matrix of a digraph G. A numerical example is given to show the efficiency of our new results.