Let
![$\mathcal{G}(\Delta^{n_{\Delta}},\ldots, 2^{n_{2}}, 1^{n_{1}},
0^{n_{0}})$](img6.png)
be the set of simple graphs with the degree sequence
![${\rm deg}(\Delta^{n_{\Delta}}, \ldots, 2^{n_{2}},
1^{n_{1}},0^{n_{0}})$](img7.png)
, and
![$\mathcal{G}^{*}(\Delta^{n_{\Delta}},\ldots, 2^{n_{2}}, 1^{n_{1}})$](img8.png)
the set of connected graphs with the degree sequence
![$\ldots, 2^{n_{2}}, 1^{n_{1}})$](img10.png)
. In this
paper, we first give the numbers of spanning tree of a bicyclic
graph as well as a tricyclic graph, and then show that some degree
sequences of graphs in
![$\mathcal{G}(2^{n_{2}}, 1^{n_{1}},
0^{n_{0}})$](img11.png)
(resp.
![$\mathcal{G}^{*}(3^{n_{3}}, 2^{n_{2}},
1^{n_{1}})$](img12.png)
,
![$\mathcal{G}^{*}(4^{n_{4}}, 2^{n_{2}}, 1^{n_{1}})$](img13.png)
and
![$\mathcal{G}^{*}(4^{n_{4}}, 3^{n_{3}}, 2^{n_{2}}, 1^{n_{1}})$](img14.png)
) are
determined by Laplacian spectra (write as
DLS for short) of
the corresponding graphs. Moreover, for the non-
DLS degree
sequences we present some
![$L$](img15.png)
-cospectral mates to indicate that
their
![$L$](img15.png)
-cospectral degree sequences do exist. By the way, all of
these extend the previous results about Laplacian spectral
determinations of some degree sequences in [23]. Besides, we revise
the references of Theorems 6 and 7 in [23].