The spectrum of eigenvalues for certain subgraphs of the k-point fixing graph
Ku, Cheng Yeaw
Wong, Kok Bin
Date of Issue2018
School of Physical and Mathematical Sciences
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.
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].