Faber-Krahn type inequality for unicyclic graphs

Details Faber-Krahn type inequality for unicyclic graphs Faber-Krahn type inequality for unicyclic graphs

2012-01-02

arxiv.org/abs/1201.0455v1

Mathematics

Combinatorics

13 pages, figures, 13 references; Linear and Multilinear algebra 2012

Scientific paper

The Faber-Krahn inequality states that the ball has minimal first Dirichlet
eigenvalue among all bounded domains with the fixed volume in $\mathbb{R}^n$.
In this paper, we investigate the similar inequality for unicyclic graphs. The
results 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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