Abstract: Let B(n,α) be the class of bicyclic graphs on n vertices with independence numberα. Let B₁(n,α) be the subclass of B(n,α) consisting of all bicyclic graphs with two edge-disjoint cycles and B₂(n,α) = B（n,α)\B₁(n,α). This paper determined the unique graph with the maximal signless Laplacian spectral radius among all graphs in B₁(n,α) and B₂(n,α), respectively. Furthermore, the upper bound of the signless Laplacian spectral radius and the extremal graph for B(n,α) were also obtained.

Key words: bicyclic graph, independence number, signless Laplacian spectral radius, bicyclic graph, independence number