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Let $A(G)$ be the adjacency matrix of $G$ and $D(G)=\\textrm{diag}(d_1^{+},d_2^{+},\\ldots,d_n^{+})$ be the diagonal matrix with outdegrees of the vertices of $G$. Then we call $Q(G)=D(G)+A(G)$ the signless Laplacian matrix of $G$. The spectral radius of $Q(G)$ is called the signless Laplacian spectral radius of $G$, denoted by $q(G)$. 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