Graphs whose Laplacian eigenvalues are almost all 1 or 2
Special MatricesWe explicitly determine all connected graphs whose Laplacian matrices have at most four eigenvalues different from 1 and 2.
Mohammadian Ali, Xu Shanshan
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On a rigidity result for the first conformal eigenvalue of the Laplacian
, 2015 Romain Petrides
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On simple eigenvalues of the fractional Laplacian under removal of small fractional capacity sets [PDF]
, 2019 Laura Abatangelo +2 more
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Eigenvalues for anisotropic p-Laplacian under a Steklov-like boundary condition [PDF]
, 2021 Luminiţa Barbu
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Global bifurcation from the eigenvalues of the p-Laplacian
, 1991 Manuel del Pino, Raúl Manásevich
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Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator [PDF]
, 2012 Rafael D. Benguria +2 more
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On the least positive eigenvalue of the Laplacian for Riemannian manifolds [PDF]
, 1977 Hajime Urakawa
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Girth and Laplacian eigenvalue distribution
Let $G$ be a connected graph of order $n$ with girth $g$. For $k=1,\dots,\min\{g-1, n-g\}$, let $n(G,k)$ be the number of Laplacian eigenvalues (counting multiplicities) of $G$ that fall inside the interval $[n-g-k+4,n]$. We prove that if $g\ge 4$, then \[ n(G,k)\le n-g. \] Those graphs achieving the bound for $k=1,2$ are determined.
Xu, Leyou, Zhou, Bo
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On Eigenvalue and Maximum Principle Type Problems Involving the p-Laplacian with Nonlinear Boundary Conditions [PDF]
Pascaline Nshimirimana +2 more
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Distribution of signless Laplacian eigenvalues and graph invariants [PDF]
, 2023 Leyou Xu, Bo Zhou
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