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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.)
##### Keywords:
graph spectrum; bipartite graphs; triangle-free graphs
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