Signed analogue of line graphs and their smallest eigenvalues

Alexander L. Gavrilyuk, Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we show that every connected signed graph with smallest eigenvalue strictly greater than (Formula presented.) 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.

Original languageEnglish
Pages (from-to)309-325
Number of pages17
JournalJournal of Graph Theory
Volume98
Issue number2
DOIs
Publication statusPublished - 2021 Sep

Keywords

  • Hoffman graph
  • line graph
  • root system
  • signed graph
  • smallest eigenvalue

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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