### The maximum signless Laplacian spectral radius of graphs with forbidden subgraphs

#### Abstract

The Brualdi-Solheid-Tur\'{a}n type problem has attracted wide attention recently. Let $\mathcal{F}$ be a set of graphs. A graph $G$ is $\mathcal{F}$-free if it does not contain any element of $\mathcal{F}$ as a subgraph. In this paper, when $\mathcal{F}_1=\{W_5, C_6\}$ and $\mathcal{F}_2=\{F_5\}$, we determine the maximum signless Laplacian spectral radius of $\mathcal{F}_i$-free graph with $n$ vertices, respectively and depict the corresponding extremal graph for $i=1, 2$.

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