Maximizing the signless Laplacian spectral radius of graphs with given diameter or cut vertices

摘要

The signless Laplacian matrix of a graph is defined to be the sum of its adjacency matrix and degree matrix. Let be the set of all the connected graphs of order n and diameter d and _n,k the set of all connected graphs with order n and k cut vertices. In this article, we determine the graphs that have the maximal signless Laplacian spectral radius and give the upper bounds of graphs in these two sets.