Regular graphs with small second largest eigenvalue. (English) Zbl 1313.05229

Koledin, Tamara; Stanić, Zoran

Appl. Anal. Discrete Math. 7, No. 2, 235-249 (2013).

The authors consider regular graphs with small second largest eigenvalue \(\lambda_2\). In particular, all triangle-free regular graphs with \(\lambda_2\leq\sqrt{2}\), all bipartite regular graphs with \(\lambda_2\leq\sqrt{3}\), and all bipartite regular graphs of degree \(3\) with \(\lambda_2\leq 2\) are determined.

Reviewer: Mirko Lepović (Kragujevac)

MSC:

05C50

Graphs and linear algebra (matrices, eigenvalues, etc.)

Keywords:

graph spectrum; bipartite graphs; triangle-free graphs