Minimum supports of eigenfunctions with the second largest eigenvalue of\n the Star graph

2019/10/03 by V. V. Kabanov, Elena V. Konstantinova, Kabanov, Vladislav +5
Engineering · Mathematics · #05B30 #05C25 #05C50 #05E15 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1910.01374

openalex publication_date 2019/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Star graph S_n, n\≥ 3, is the Cayley graph on the symmetric group\nSym_n generated by the set of transpositions (12),(13),\…,(1n) . In\nthis work we study eigenfunctions of S_n corresponding to the second largest\neigenvalue n-2. For n\≥ 8 and n=3, we find the minimum cardinality of\nthe support of an eigenfunction of S_n corresponding to the second largest\neigenvalue and obtain a characterization of eigenfunctions with the minimum\ncardinality of the support.\n

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