The set of all non-increasing nonnegative integers sequence $\pi=$
($d(v_1 ),$ $d(v_2 ),$ $...,$ $d(v_n )$) is denoted by $NS_n$.
A sequence
$\pi\in NS_n$ is said to be graphic if it is the degree sequence of
a simple graph $G$ on $n$ vertices, and such a graph $G$ is called a
realization of $\pi$. The set of all graphic sequences in $NS_n$ is
denoted by $GS_n$. A graphical sequence $\pi$ is potentially
$H$-graphical if there is a realization of $\pi$ containing $H$ as a
subgraph, while $\pi$ is forcibly $H$-graphical if every realization
of $\pi$ contains $H$ as a subgraph. Let $K_k$ denote a complete
graph on $k$ vertices. Let $K_{m}-H$ be the graph obtained from
$K_{m}$ by removing the edges set $E(H)$ of the graph $H$ ($H$ is a
subgraph of $K_{m}$). This paper summarizes briefly some recent
results on potentially $K_{m}-G$-graphic sequences and give a useful
classification for determining $\sigma(H,n)$.