The signless Laplacian matrix of a graphG is defined to be the sum of its adjacency matrix and degree diagonal matrix,and its eigenvalues are called Q-eigenvalues of G.A Q-eigenvalue of a graph G is called a Q-main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero.In this work,all trees,unicyclic graphs and bicyclic graphs with exactly two Q-main eigenvalues are determined.
