Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2512.04836 |
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Inhaltsangabe:
- This paper investigates limit points of the deformed Laplacian matrix, which merges the Laplacian and signless Laplacian matrices of a graph through a quadractic one-parameter family of matrices. First, we show that any value greater or equal to 1 is a deformed Laplacian limit point (for different values of the parameter $s$) using a simple family of trees. Second, we define $(T_k)_{k \in \mathbb{N}}$ the Shearer's sequence of caterpillars for $λ>1$ and we present a convergence criterion based on Shearer's approach. Our main result is that for any fixed value $λ_0>1$ there exists a unique value $0<s^* <\sqrt{λ_0} -1$ such that, and for any $s \in (0,s^*)$ the interval $[λ_0, \; +\infty)$ is entirely formed by $s$-deformed Laplacian limit points (for the same value of $s$). Finally, we provide some numerical data exploring the limit properties.