On the Spectra of Simplicial Rook Graphs

@article{Martin2015OnTS,
  title={On the Spectra of Simplicial Rook Graphs},
  author={Jeremy L. Martin and Jennifer D. Wagner},
  journal={Graphs and Combinatorics},
  year={2015},
  volume={31},
  pages={1589-1611}
}
The simplicial rook graph SR(d, n) is the graph whose vertices are the lattice points in the nth dilate of the standard simplex in R, with two vertices adjacent if they differ in exactly two coordinates. We prove that the adjacency and Laplacian matrices of SR(3, n) have integral spectra for every n. We conjecture that SR(d, n) is integral for all d and n… CONTINUE READING