  Let $F_{p,q}$ be the generalized friendship graph $K_1\bigvee (pK_q)$ on
$pq+1$ vertices obtained by joining a vertex to all vertices of $p$ disjoint
copies of the complete graph $K_q$ on $q$ vertices. In this paper, we prove
that $F_{p,q}$ is determined by its normalized Laplacian spectrum if and only
if $q\ge 2$, or $q=1$ and $p\le 2$.
