Notes on simplicial rook graphs
Notes on simplicial rook graphs
The simplicial rook graph $$\mathrm{SR}(m,n)$$ 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 $$\mathrm{SR}(m,n)$$ has integral eigenvalues, and smallest eigenvalue $$s = \max …