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

MSC:
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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