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.
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