A spectral characterization of the s-clique extension of the square grid graphs

In this paper we show that for integers $sgeq2$, $tgeq1$, any co-edge-regular graph which is cospectral with the $s$-clique extension of the $ttimes t$-grid is the $s$-clique extension of the $ttimes t$-grid, if $t$ is large enough. Gavrilyuk and Koolen used a weaker version of this result to show that the Grassmann graph $J_q(2D,D)$ is characterized by its intersection array as a distance-regular graph, if $D$ is large enough.