  A regular graph is co-edge regular if there exists a constant $\mu$ such that
any two distinct and non-adjacent vertices have exactly $\mu$ common neighbors.
In this paper, we show that for integers $s\ge 2$ and $n$ large enough, any
co-edge-regular graph which is cospectral with the $s$-clique extension of the
triangular graph $T((n)$ is exactly the $s$-clique extension of the triangular
graph $T(n)$.
