The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles
Document Type
Article
Publication Date
12-1-2022
Abstract
Let S-n be the symmetric group on n] = {1, 2,..., n} and C-n(r) be the set of all r -cycles in S-n that do not fix 1, i.e., C-n(r) = {alpha is an element of S-n vertical bar alpha(1) not equal 1 and ais an r-cycle}. In this paper, we give a reduction formula of the eigenvalues of the Cayley graph Gamma(S-n, C-n(r)). Then we apply it to determine all the eigenvalues of the Cayley graph Gamma(S-n, C-n(r)) for r = 3, n - 1 and n.
Keywords
Cayley graph, Symmetric group, Spectrum integrality
Divisions
MathematicalSciences
Publication Title
Bulletin of the Iranian Mathematical Society
Volume
48
Issue
6
Publisher
Springer Singapore
Publisher Location
#04-01 CENCON I, 1 TANNERY RD, SINGAPORE 347719, SINGAPORE
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