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On the partitions associated with the smallest eigenvalues of certain Cayley graphs on symmetric group generated by cycles

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Abstract Let S n be the symmetric group on [ n ] = { 1 , 2 , … , n } and Z n ( s ) = {… Click to show full abstract

Abstract Let S n be the symmetric group on [ n ] = { 1 , 2 , … , n } and Z n ( s ) = { α ∈ S n : α is an s -cycle } where 2 ≤ s ≤ n . In this paper, we determine all the partitions associated with the smallest eigenvalues of the Cayley graph Γ ( S n , Z n ( s ) ) for s = 3 .

Keywords: smallest eigenvalues; eigenvalues certain; symmetric group; associated smallest; partitions associated

Journal Title: Linear Algebra and its Applications
Year Published: 2021

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