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The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles

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 Ga...

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Main Authors: Lau, Terry Shue Chien, Wong, Kok Bin
Format: Article
Published: Springer Singapore 2022
Subjects:
QA Mathematics
Online Access:http://eprints.um.edu.my/40457/
https://doi.org/10.1007/s41980-022-00680-5
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spelling my.um.eprints.404572025-01-17T02:15:56Z http://eprints.um.edu.my/40457/ The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles Lau, Terry Shue Chien Wong, Kok Bin QA Mathematics 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. Springer Singapore 2022-12 Article PeerReviewed Lau, Terry Shue Chien and Wong, Kok Bin (2022) The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles. Bulletin of the Iranian Mathematical Society, 48 (6). pp. 2981-2993. ISSN 1017-060X, DOI https://doi.org/10.1007/s41980-022-00680-5 <https://doi.org/10.1007/s41980-022-00680-5>. https://doi.org/10.1007/s41980-022-00680-5 10.1007/s41980-022-00680-5
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
spellingShingle QA Mathematics
Lau, Terry Shue Chien
Wong, Kok Bin
The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles
description 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.
format Article
author Lau, Terry Shue Chien
Wong, Kok Bin
author_facet Lau, Terry Shue Chien
Wong, Kok Bin
author_sort Lau, Terry Shue Chien
title The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles
title_short The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles
title_full The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles
title_fullStr The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles
title_full_unstemmed The Spectrum of Cayley Graphs on Symmetric Group Generated by Certain Subset of r-Cycles
title_sort spectrum of cayley graphs on symmetric group generated by certain subset of r-cycles
publisher Springer Singapore
publishDate 2022
url http://eprints.um.edu.my/40457/
https://doi.org/10.1007/s41980-022-00680-5
_version_ 1825160579147366400
score 13.244413

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