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math.CO2026
Weighted discrete tori and weighted trigonometric sums
Shuofeng Huang, Chengjie Yu
In this paper, we obtain a weighted trigonometric summation formula which is an extension of the trigonometric summation formula by Grigor'yan, Lin and Yau \cite{GLY}.
math.CO2026
An extension of Katsuda-Urakawa's Faber-Krahn inequality
Wankai He, Chengjie Yu
In this paper, motivated by our previous work \cite{HY}, we prove that the minimum of the first Dirichlet eigenvalues for the normalized combinatorial -Laplacian on connected fi…
math.CO2026
Faber-Krahn inequalities for first Dirichlet eigenvalues of combinatorial -Laplacian on graphs with boundary
Wankai He, Chengjie Yu
In this paper, we obtain sharp Faber-Krahn inequalities for the first Dirichlet eigenvalue of the combinatorial -Laplacian on connected graphs with a fixed number of vertices or…