Alternating sign property of the perfect matching derangement graph
It was conjectured in the monograph 9] by Godsil and Meagher and in the article 10] by Lindzey that the per-fect matching derangement graph M2n possesses the alter-nating sign property, that is, for any integer partition A = (A1, . . . , Ar) diamond -n, the sign of the eigenvalue eta lambda of M2n i...
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my.um.eprints.393482023-07-11T06:15:49Z http://eprints.um.edu.my/39348/ Alternating sign property of the perfect matching derangement graph Koh, Zhi Kang Samuel Ku, Cheng Yeaw Wong, Kok Bin QA Mathematics It was conjectured in the monograph 9] by Godsil and Meagher and in the article 10] by Lindzey that the per-fect matching derangement graph M2n possesses the alter-nating sign property, that is, for any integer partition A = (A1, . . . , Ar) diamond -n, the sign of the eigenvalue eta lambda of M2n is given by sign(eta lambda) = (-1)n-lambda 1 . In this paper, we prove that the con-jecture is true. Our approach yields a recurrence formula for the eigenvalues of the perfect matching derangement graph as well as a new recurrence formula for the eigenvalues of the permutation derangement graph.(c) 2022 Elsevier Inc. All rights reserved. Elsevier 2023-02 Article PeerReviewed Koh, Zhi Kang Samuel and Ku, Cheng Yeaw and Wong, Kok Bin (2023) Alternating sign property of the perfect matching derangement graph. Journal of Combinatorial Theory, Series A, 194. ISSN 0097-3165, DOI https://doi.org/10.1016/j.jcta.2022.105706 <https://doi.org/10.1016/j.jcta.2022.105706>. 10.1016/j.jcta.2022.105706 |
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QA Mathematics Koh, Zhi Kang Samuel Ku, Cheng Yeaw Wong, Kok Bin Alternating sign property of the perfect matching derangement graph |
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It was conjectured in the monograph 9] by Godsil and Meagher and in the article 10] by Lindzey that the per-fect matching derangement graph M2n possesses the alter-nating sign property, that is, for any integer partition A = (A1, . . . , Ar) diamond -n, the sign of the eigenvalue eta lambda of M2n is given by sign(eta lambda) = (-1)n-lambda 1 . In this paper, we prove that the con-jecture is true. Our approach yields a recurrence formula for the eigenvalues of the perfect matching derangement graph as well as a new recurrence formula for the eigenvalues of the permutation derangement graph.(c) 2022 Elsevier Inc. All rights reserved. |
| format |
Article |
| author |
Koh, Zhi Kang Samuel Ku, Cheng Yeaw Wong, Kok Bin |
| author_facet |
Koh, Zhi Kang Samuel Ku, Cheng Yeaw Wong, Kok Bin |
| author_sort |
Koh, Zhi Kang Samuel |
| title |
Alternating sign property of the perfect matching derangement graph |
| title_short |
Alternating sign property of the perfect matching derangement graph |
| title_full |
Alternating sign property of the perfect matching derangement graph |
| title_fullStr |
Alternating sign property of the perfect matching derangement graph |
| title_full_unstemmed |
Alternating sign property of the perfect matching derangement graph |
| title_sort |
alternating sign property of the perfect matching derangement graph |
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Elsevier |
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2023 |
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http://eprints.um.edu.my/39348/ |
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1772811758354825216 |
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13.201949 |