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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| Format: | Article |
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Elsevier
2023
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| Online Access: | http://eprints.um.edu.my/39348/ |
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| Summary: | 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. |
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