  Let $F_k$ denote the $k$-fan consisting of $k$ triangles which intersect in
exactly one common vertex, and $S_{n,k}$ the complete split graph of order $n$
consisting of a clique on $k$ vertices and an independent set on the remaining
vertices in which each vertex of the clique is adjacent to each vertex of the
independent set. In this paper, it is shown that $S_{n,k}$ is the unique graph
attaining the maximum signless Laplacian spectral radius among all graphs of
order $n$ containing no $F_k$, provided that $k\geq 2$ and $n\geq 3k^2-k-2$.

Combinatorics