On graphs whose smallest eigenvalue is at least \(-1-\sqrt 2\)
This paper shows that if the smallest eigenvalue of a graph \(H\) exceeds a fixed number larger than the smallest root \((\approx- 2.4812)\) of the polynomial \(x^3+ 2x^2- 2x- 2\), and if every vertex of \(H\) has sufficiently large valency, then the smallest eigenvalue of \(H\) is at least \(-1-\sqrt 2\) and the structure of \(H\) is completely characterized through a new generalization of line graphs.
scientific article; zbMATH DE number 803762