The signless Laplacian spectral radius of 2K₃-free graphs

Let 2K₃ denote the disjoint union of two triangles. Given a graph H, a graph is said to be H-free if it does not contain H as a subgraph. In spectral extremal graph theory, it is interesting to determine the maximum (signless Laplacian) spectral radius of H-free graphs. In this paper, we characterize the unique extremal graph with the maximum signless Laplacian spectral radius among all 2K₃-free graphs of order n≥44.