  The generalized $k$-connectivity of a graph $G$, denoted by $\kappa_k(G)$, is
the minimum number of internally edge disjoint $S$-trees for any $S\subseteq
V(G)$ and $|S|=k$. The generalized $k$-connectivity is a natural extension of
the classical connectivity and plays a key role in applications related to the
modern interconnection networks. The godan graph $EA_n$ is a kind of Cayley
graphs which posses many desirable properties. In this paper, we shall study
the generalized 4-connectivity of $EA_n$ and show that $\kappa_4(EA_n)=n-1$ for
$n\ge 3$.
