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The absolute values of the perfect matching derangement graph's eigenvalues almost follow the lexicographic order of partitions.

Authors :
Zhang, Meiqiao
Dong, Fengming
Source :
Discrete Mathematics. Nov2024, Vol. 347 Issue 11, pN.PAG-N.PAG. 1p.
Publication Year :
2024

Abstract

In 2013, Ku and Wong showed that for any partitions μ and μ ′ of a positive integer n with the same first part u and the lexicographic order μ ◃ μ ′ , the eigenvalues ξ μ and ξ μ ′ of the derangement graph Γ n have the property | ξ μ | ≤ | ξ μ ′ | , where the equality holds if and only if u = 3 and all other parts are less than 3. In this article, we obtain an analogous conclusion on the eigenvalues of the perfect matching derangement graph M 2 n of K 2 n by finding a new recurrence formula for the eigenvalues of M 2 n. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
0012365X
Volume :
347
Issue :
11
Database :
Academic Search Index
Journal :
Discrete Mathematics
Publication Type :
Academic Journal
Accession number :
178832086
Full Text :
https://doi.org/10.1016/j.disc.2024.114188