Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423549 | Discrete Mathematics | 2011 | 16 Pages |
For any integer n greater than or equal to two, two intimately related graphs on the vertices of the n-dimensional cube are introduced. All of their eigenvalues are found to be integers, and the largest and the smallest ones are also determined. As a byproduct, certain kind of generating function for their spectra is introduced and shown to be quite effective to compute the eigenvalues of some broader class of adjacency matrices of graphs.
⺠Two graphs on the hypercube are introduced. ⺠All of their eigenvalues are found to be integers. ⺠Their largest and smallest eigenvalues are determined. ⺠Crucial role is played by a generating function for the spectra of each graph. ⺠A possible generalization to some other graphs on the hypercube is indicated.