The signless Laplacian spectral radius of graphs with given diameter

In this paper, we show that among all connected graphs of order n with diameter D, the graph G*(D) has maximal signless Laplacian spectral radius, where G*D is obtained from Kn-D V (K-2) over bar by identifying one endvertex of path with length l(1) at u and one endvertex of path with length l(2) at v, respectively, where u, v are two vertices of (K-2) over bar, vertical bar l(1) - 1(2)vertical bar <= 1.