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
Publication Title
Bulletin of the Iranian Mathematical Society
Recommended Citation
Lau, Terry Shue Chien and Wong, Kok Bin, "The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles" (2022). Research Publications (2021 to 2025). 1974.
https://knova.um.edu.my/research_publications_2021_2025/1974
Divisions
MathematicalSciences
Volume
48
Issue
6
Publisher
Springer Singapore
Publisher Location
#04-01 CENCON I, 1 TANNERY RD, SINGAPORE 347719, SINGAPORE