Abstract
The Faber–Krahn inequality is related to the smallest nonzero eigenvalue of the Laplacian operator with Dirichlet boundary condition on a bounded domain in ℝ n . In this article, we investigate some properties of the first Dirichlet eigenvalue of unicyclic graphs. These results are used to show that the Faber–Krahn type inequality also holds for unicyclic graphs with a given graphic unicyclic degree sequence with minor conditions.
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