Suppose that $G$ is a simple connected graph with the vertex set $V(G)=\{v_1,v_2,$ $\cdots,v_n\}$. Then the adjacency matrix of $G$ is $A(G)=(a_{ij})_{n\times n}$, where $a_{ij}=1$ if $v_i$ is adjacent to $v_j$, and otherwise $a_{ij}=0$. The degree matrix $D(G)={\rm diag}(d_{G}(v_1), d_{G}(v_2),\cdots,d_{G}(v_n))$, where $d_{G}(v_i)$ denotes the degree of $v_i$ in the graph $G(1\leq i\leq n)$. The matrix $Q(G)=D(G)+A(G)$ is the signless Laplacian matrix of $G$. Since $Q(G)$ is positive semidefinite, its eigenvalues can be arranged as $\lambda_1(G)\geq \lambda_2(G)\geq \cdots \geq \lambda_n(G)\geq 0$, where $\lambda_n(G)$ is the least signless Laplacian eigenvalue of $G$. The least signless Laplacian eigenvalues is investigated for the complements of graphs and the state of art of the relevant issues is summarized. By virtue of two graft transformations obtained by us, the unique connected graph is characterized, whose least signless Laplacian eigenvalue is minimum among the complements of all bicyclic graphs.