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Signed analogue of line graphs and their smallest eigenvalues
Author(s) -
Gavrilyuk Alexander L.,
Munemasa Akihiro,
Sano Yoshio,
Taniguchi Tetsuji
Publication year - 2021
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22699
Subject(s) - mathematics , combinatorics , line graph , signed graph , discrete mathematics , eigenvalues and eigenvectors , graph , physics , quantum mechanics
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.