Geodesic
Notes on simplicial rook graphs
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 4, pp. 783-799.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $s = \max(-n,-{{m}\choose{2}})$, 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.
Classification : 05C50, 05C25
Keywords: simplicial rook graph, graph spectra, integral graph, Johnson graph, equitable partition 
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     title = {Notes on simplicial rook graphs},
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Brouwer, Andries E.; Cioabă, Sebastian M.; Haemers, Willem H.; Vermette, Jason R. Notes on simplicial rook graphs. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 4, pp. 783-799. http://geodesic.mathdoc.fr/item/JAC_2016__43_4_a6/