Geodesic
Note on exact values of multiplicities of eigenvalues of the Star graph
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 92-100

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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.
Keywords: Cayley graphs; Star graph; graph spectrum; eigenvalues. 
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     author = {Ekaterina N. Khomyakova and Elena V. Konstantinova},
     title = {Note on exact values of multiplicities of eigenvalues of the {Star} graph},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {92--100},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a53/}
}
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Ekaterina N. Khomyakova; Elena V. Konstantinova. Note on exact values of multiplicities of eigenvalues of the Star graph. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 92-100. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a53/