Notes on simplicial rook graphs
نویسندگان
چکیده
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,− ( m 2 ) ), 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.
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