Signed analogue of line graphs and their smallest eigenvalues. Issue 2 (8th June 2021)

• Record Type: Journal Article
• Authors: Gavrilyuk, Alexander L.; Munemasa, Akihiro; Sano, Yoshio; Taniguchi, Tetsuji
• Is Part Of: Journal of graph theory. Volume 98:Issue 2(2021)
• Page Start: 309
• Page End: 325
• Publication Date: 2021-06-08
• Subjects: Hoffman graph -- line graph -- root system -- smallest eigenvalue -- signed graph; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22699
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: In this article, 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.