  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 $\sigma(H,n)$.

Combinatorics