Edge-signed graphs with smallest eigenvalue greater than -2

Gary Greaves, Jack Koolen, Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

We give a structural classification of edge-signed graphs with smallest eigenvalue greater than -2. We prove a conjecture of Hoffman about the smallest eigenvalue of the line graph of a tree that was stated in the 1970s. Furthermore, we prove a more general result extending Hoffman's original statement to all edge-signed graphs with smallest eigenvalue greater than -2. Our results give a classification of the special graphs of fat Hoffman graphs with smallest eigenvalue greater than -3.

Original languageEnglish
Pages (from-to)90-111
Number of pages22
JournalJournal of Combinatorial Theory. Series B
Volume110
DOIs
Publication statusPublished - 2015 Jan 1

Keywords

  • Hoffman conjecture
  • Hoffman graphs
  • Line graphs
  • Signed graphs
  • Smallest eigenvalue

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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