The simplicial rook graph SR(m,n) is the graph of which the vertices
are the sequences of nonnegative integers of length m summing to n, where
two such sequences are adjacent when they differ in precisely two places. We
show that SR(m,n) has integral eigenvalues, and smallest eigenvalue s=max(−n,−(2m)), and that this graph has a large part of its
spectrum in common with the Johnson graph J(m+n−1,n). We determine the
automorphism group and several other properties