The spectrum of eigenvalues for certain subgraphs of the k-point fixing graph
Let Sn be the symmetric group on n-points. The k-point fixing graph F(n, k) is defined to be the graph with vertex set Sn and two vertices g, h of F(n, k) are joined if and only if gh−1 fixes exactly k points. In this paper, we give a recurrence formula for the eigenvalues of a class of regular subg...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2018
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| Online Access: | https://hdl.handle.net/10356/89348 http://hdl.handle.net/10220/44907 |
| _version_ | 1811680331459198976 |
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| author | Ku, Cheng Yeaw Lau, Terry Wong, Kok Bin |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Ku, Cheng Yeaw Lau, Terry Wong, Kok Bin |
| author_sort | Ku, Cheng Yeaw |
| collection | NTU |
| description | Let Sn be the symmetric group on n-points. The k-point fixing graph F(n, k) is defined to be the graph with vertex set Sn and two vertices g, h of F(n, k) are joined if and only if gh−1 fixes exactly k points. In this paper, we give a recurrence formula for the eigenvalues of a class of regular subgraphs of F(n, k). By using this recurrence formula, we will determine the smallest eigenvalues for this class of regular subgraphs of F(n, 1) for sufficiently large n. |
| first_indexed | 2024-10-01T03:23:21Z |
| format | Journal Article |
| id | ntu-10356/89348 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:23:21Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/893482023-02-28T19:36:11Z The spectrum of eigenvalues for certain subgraphs of the k-point fixing graph Ku, Cheng Yeaw Lau, Terry Wong, Kok Bin School of Physical and Mathematical Sciences Cayley Graphs Arrangement Graph Let Sn be the symmetric group on n-points. The k-point fixing graph F(n, k) is defined to be the graph with vertex set Sn and two vertices g, h of F(n, k) are joined if and only if gh−1 fixes exactly k points. In this paper, we give a recurrence formula for the eigenvalues of a class of regular subgraphs of F(n, k). By using this recurrence formula, we will determine the smallest eigenvalues for this class of regular subgraphs of F(n, 1) for sufficiently large n. Accepted version 2018-05-30T06:41:32Z 2019-12-06T17:23:29Z 2018-05-30T06:41:32Z 2019-12-06T17:23:29Z 2018 Journal Article Ku, C. Y., Lau, T., & Wong, K. B. (2018). The spectrum of eigenvalues for certain subgraphs of the k-point fixing graph. Linear Algebra and its Applications, 543, 72-91. 0024-3795 https://hdl.handle.net/10356/89348 http://hdl.handle.net/10220/44907 10.1016/j.laa.2017.12.018 en Linear Algebra and its Applications © 2017 Elsevier Inc. This is the author created version of a work that has been peer reviewed and accepted for publication by Linear Algebra and Its Applications, Elsevier Inc. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.laa.2017.12.018]. 18 p. application/pdf |
| spellingShingle | Cayley Graphs Arrangement Graph Ku, Cheng Yeaw Lau, Terry Wong, Kok Bin The spectrum of eigenvalues for certain subgraphs of the k-point fixing graph |
| title | The spectrum of eigenvalues for certain subgraphs of the k-point fixing graph |
| title_full | The spectrum of eigenvalues for certain subgraphs of the k-point fixing graph |
| title_fullStr | The spectrum of eigenvalues for certain subgraphs of the k-point fixing graph |
| title_full_unstemmed | The spectrum of eigenvalues for certain subgraphs of the k-point fixing graph |
| title_short | The spectrum of eigenvalues for certain subgraphs of the k-point fixing graph |
| title_sort | spectrum of eigenvalues for certain subgraphs of the k point fixing graph |
| topic | Cayley Graphs Arrangement Graph |
| url | https://hdl.handle.net/10356/89348 http://hdl.handle.net/10220/44907 |
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