This article is cited in 4 papers

Discrete mathematics and mathematical cybernetics

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

Ekaterina N. Khomyakova^a, Elena V. Konstantinova<sup>ba

a</sup> Novosibirsk State University, 2, Pirogova st., 630090, Novosibirsk, Russia
^b Sobolev Institute of Mathematics, 4, Koptyug av., 630090, Novosibirsk, Russia

Abstract: 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.

UDC: 519.1

MSC: 05C25, 05C50, 05E10

Received November 25, 2014, published February 20, 2015

Language: English

DOI: 10.17377/semi.2015.12.008