2020/03/12 by Alexander L. Gavrilyuk, Akihiro Munemasa, Gavrilyuk, Alexander L. +5 · 1 citation
Computer Science · Mathematics · #05C22 #05C50 #15A18 #15B57 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #math.CO #msc:05C22 #msc:05C50 #msc:15A18 #msc:15B57
paper · pdf · doi:10.48550/arxiv.2003.05578
20 pages, minor revision
openalex publication_date 2020/03/12 · arxiv created 2021/04/05 · arxiv updated 2021/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we show that every connected signed graph with smallest eigenvalue strictly greater than -2 and large enough minimum degree is switching equivalent to a complete graph. This is a signed analogue of a theorem of Hoffman. The proof is based on what we call Hoffman's limit theorem which we formulate for Hermitian matrices, and also the extension of the concept of Hoffman graph and line graph for the setting of signed graphs.