Note on exact values of multiplicities of eigenvalues of the Star graph

The Star graph is the Cayley graph on the symmetric group $Sym_n$ generated by the set of transpositions $\{(1 2),(1 3),\ldots,(1 n)\}$. A Chapuy–Feray combinatorial approach is used to obtain multiplicities of eigenvalues. Exact values are calculated up to $n=10$ and compared with lower bounds on multiplicities of eigenvalues for this graph.