The signless Laplacian spectral radius of graphs with given diameter - Feng, Li-Hua; Yu, Gui-Hai (Utilitas Mathematica, 2010)
In this paper, we show that among all connected graphs of order n with diameter D, the graph GD* has maximal signless Laplacian spectral radius, where GD*, is obtained from Kn-D V K̄2 by identifying one endvertex of path with length l 1 at u and one endvertex of path with length l2 at v, respectively, where u, v are two vertices of K̄2, |l1 - l22| ≤ 1.