Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/164642
Title: Alternating sign property of the perfect matching derangement graph
Authors: Koh, Samuel Zhi Kang
Ku, Cheng Yeaw
Wong, Kok Bin
Keywords: Science::Physics
Issue Date: 2023
Source: Koh, S. Z. K., Ku, C. Y. & Wong, K. B. (2023). Alternating sign property of the perfect matching derangement graph. Journal of Combinatorial Theory. Series A, 194, 105706-. https://dx.doi.org/10.1016/j.jcta.2022.105706
Journal: Journal of Combinatorial Theory. Series A
Abstract: It was conjectured in the monograph [9] by Godsil and Meagher and in the article [10] by Lindzey that the perfect matching derangement graph M2n possesses the alternating sign property, that is, for any integer partition λ=(λ1,…,λr)⊢n, the sign of the eigenvalue ηλ of M2n is given by sign(ηλ)=(−1)n−λ1. In this paper, we prove that the conjecture 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.
URI: https://hdl.handle.net/10356/164642
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2022.105706
Schools: School of Physical and Mathematical Sciences 
Rights: © 2022 Elsevier Inc. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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