  In the present paper, exterior algebraic shifting and symmetric algebraic
shifting of bipartite graphs and chordal graphs are studied. First, we will
determine the symmetric algebraic shifted graph of complete bipartite graphs.
It turns out that, for $a>3$ and $b>3$, the exterior algebraic shifted graph of
the complete bipartite graph $K_{a,b}$ of size $a,b$ is different from the
symmetric algebraic shifted graph of $K_{a,b}$. Second, we will show that the
exterior algebraic shifted graph of any chordal graph $G$ is coincident with
the symmetric algebraic shifted graph of $G$.
