  This paper surveys some recent results and progress on the extremal prob-
lems in a given set consisting of all simple connected graphs with the same
graphic degree sequence. In particular, we study and characterize the extremal
graphs having the maximum (or minimum) values of graph invariants such as
(Laplacian, p-Laplacian, signless Laplacian) spectral radius, the first
Dirichlet eigenvalue, the Wiener index, the Harary index, the number of
subtrees and the chromatic number etc, in given sets with the same tree,
unicyclic, graphic degree sequences. Moreover, some conjectures are included.
