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Wankai He

Publications and source records attributed to Wankai He.

2 recordsLinked to original sources

arXiv2026

An extension of Katsuda-Urakawa's Faber-Krahn inequality

In this paper, motivated by our previous work \cite{HY}, we prove that the minimum of the first Dirichlet eigenvalues for the normalized combinatorial $p$-Laplacian on connected finite graphs with boundary consisting of $n$ edges is only achieved by the tadpole graph $T_{n,3}$. This result extends the Faber-Krahn inequality of Katsuda-Urakawa \cite{KU} to normalized combinatorial $p$-Laplacians. Our argument is much simpler than that of Katsuda-Urakawa.

math.CO↗

arXiv2026

Faber-Krahn inequalities for first Dirichlet eigenvalues of combinatorial $p$-Laplacian on graphs with boundary

In this paper, we obtain sharp Faber-Krahn inequalities for the first Dirichlet eigenvalue of the combinatorial $p$-Laplacian on connected graphs with a fixed number of vertices or with a fixed number of edges. More precisely, we show that the minimum of the first $p$-Dirichlet eigenvalues of connected graphs with boundary that consist of $n$ vertices or $n$ edges is achieved only on the tadpole graph $T_{n,3}$ when $p>1$.

math.CO↗