A family of graphs that are determined by their normalized Laplacian spectra

Let Fp,q be the generalized friendship graph K1⋁(pKq) on pq+1 vertices obtained by joining a vertex to all vertices of p disjoint copies of the complete graph Kq on q vertices. In this paper, we prove that Fp,q is determined by its normalized Laplacian spectrum if and only if q≥2, or q=1 and p≤2.