Catalogue of the Star graph eigenvalue multiplicities

The Star graph Sn, n >= 2, is the Cayley graph over the symmetric group Symn generated by transpositions (1 i), 2 <= i <= n. This set of transpositions plays an important role in the representation theory of the symmetric group. The spectrum of Sn contains all integers from -(n - 1) to n - 1, and also zero for n >= 4. In this paper we observe methods for getting explicit formulas of eigenvalue multiplicities in the Star graphs Sn, present such formulas for the eigenvalues +/-(n - k), where 2 <= k <= 12, and finally collect computational results of all eigenvalue multiplicities for n <= 50 in the catalogue.