The spectrum of eigenvalues for certain subgraphs of the k -point fixing graph

Document Type

Article

Publication Date

1-1-2018

Abstract

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.

Keywords

Arrangement graph, Cayley graphs, Symmetric group

Divisions

MathematicalSciences

Publication Title

Linear Algebra and its Applications

Volume

543

Publisher

Elsevier

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