LetW(n;q,m1,m2)be the unicyclic graph withnvertices obtained by attaching two paths of lengthsm1andm2at two adjacent vertices of cycleCq. LetU(n;q,m1,m2,…,ms)be the unicyclic graph withnvertices obtained by attachingspaths of lengthsm1,m2,…,msat the same vertex of cycleCq. In this paper, we prove thatW(n;q,m1,m2)andU(n;q,m1,m2,…,ms)are determined by their Laplacian spectra whenqis even.
On the spectral characterization of some unicyclic graphs