  Let $K_m-H$ be the graph obtained from $K_m$ by removing the edges set $E(H)$
of $H$ where $H$ is a subgraph of $K_m$. In this paper, we characterize the
potentially $K_5-P_4$ and $K_5-Y_4$-graphic sequences where $Y_4$ is a tree on
5 vertices and 3 leaves.
