  A sequence $S$ is potentially $K_{m}-H$-graphical if it has a realization
containing a $K_{m}-H$ as a subgraph. Let $\sigma(K_{m}-H, n)$ denote the
smallest degree sum such that every $n$-term graphical sequence $S$ with
$\sigma(S)\geq \sigma(K_{m}-H, n)$ is potentially $K_{m}-H$-graphical. In this
paper, we determine $\sigma (K_{r+1}-(kP_2\bigcup tK_2), n)$ for $n\geq 4r+10,
r+1 \geq 3k+2t, k+t \geq 2,k \geq 1, t \geq 0$ .
