The multi-fan graphs are determined by their Laplacian spectra

A multi-fan graph   is a graph of the form (Pn1+Pn2+⋯+Pnk)×b(Pn1+Pn2+⋯+Pnk)×b, where b   is a universal vertex, and Pn1+Pn2+⋯+PnkPn1+Pn2+⋯+Pnk is the disjoint union of paths Pni(ni⩾1)Pni(ni⩾1) for i=1,2,…,ki=1,2,…,k. In particular, if k=1k=1, the multi-fan graph Pn1×bPn1×b is the classical fan graph Fn1+1Fn1+1. It is proved that all the multi-fan graphs are determined by their Laplacian spectra.