  Let $G$ be an unicyclic graph of order $n$ and let $Q_G(x)=
det(xI-Q(G))={matrix} \sum_{i=1}^n (-1)^i \varphi_i x^{n-i}{matrix}$ be the
characteristic polynomial of the signless Laplacian matrix of a graph $G$. We
give some transformations of $G$ which decrease all signless Laplacian
coefficients in the set $\mathcal{G}(n,m)$. $\mathcal{G}(n,m)$ denotes all
n-vertex unicyclic graphs with matching number $m$. We characterize the graphs
which minimize all the signless Laplacian coefficients in the set
$\mathcal{G}(n,m)$ with odd (resp. even) girth. Moreover, we find the extremal
graphs which have minimal signless Laplacian coefficients in the set
$\mathcal{G}(n)$ of all $n$-vertex unicyclic graphs with odd (resp. even)
girth.
