Abstract: The signless Laplacian matrix of a graph G 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 tricyclic graphs with exactly two Q-main eigenvalues are determined.

Key words: signless Laplacian matrix, Q-main eigenvalue, tricyclic graph