Spectrum of Signless 1-Laplacian on Simplicial Complexes
Copyright policy )Spectrum of Signless 1-Laplacian on Simplicial Complexes
We introduce the signless 1-Laplacian and the dual Cheeger constant on simplicial complexes. The connection of its spectrum to the combinatorial properties like independence number, chromatic number and dual Cheeger constant is investigated. Our estimates can be comparable to Hoffman's bounds on Laplacian eigenvalues of simplicial complexes. An interesting inequality involving multiplicity of the largest eigenvalue, independence number and chromatic number is provided, which could be regarded as a variant version of Lovász sandwich theorem. Also, the behavior of 1-Laplacian under the topological operations of wedge and duplication of motifs is studied. The Courant nodal domain theorem in spectral theory is extended to the setting of signless 1-Laplacian on complexes.
- Chinese Academy of Sciences China (People's Republic of)
- Academy of Mathematics and Systems Science China (People's Republic of)
- Hunan Women'S University China (People's Republic of)
- Peking University China (People's Republic of)
dual Cheeger constant, Combinatorial aspects of simplicial complexes, Mathematical analysis, Quantum mechanics, Graph, Mathematics - Spectral Theory, chromatic number, FOS: Mathematics, Mathematics - Combinatorics, independence number, Spectrum (functional analysis), Simplicial complex, Spectral Theory (math.SP), Eigenvalues and eigenvectors, Persistent Homology, Nonlinear spectral theory, nonlinear eigenvalue problems, Physics, Graph Spectra and Topological Indices, Symplectic Topology and Knot Invariants, Discrete mathematics, Computer science, Programming language, Topological Data Analysis in Science and Engineering, Multiplicity (mathematics), Computational Theory and Mathematics, Laplace operator, Combinatorics, Computer Science, Physical Sciences, Chromatic scale, Independence number, Combinatorics (math.CO), Geometry and Topology, Laplacian matrix, Variational methods for eigenvalues of operators, Mathematics, Constant (computer programming)
dual Cheeger constant, Combinatorial aspects of simplicial complexes, Mathematical analysis, Quantum mechanics, Graph, Mathematics - Spectral Theory, chromatic number, FOS: Mathematics, Mathematics - Combinatorics, independence number, Spectrum (functional analysis), Simplicial complex, Spectral Theory (math.SP), Eigenvalues and eigenvectors, Persistent Homology, Nonlinear spectral theory, nonlinear eigenvalue problems, Physics, Graph Spectra and Topological Indices, Symplectic Topology and Knot Invariants, Discrete mathematics, Computer science, Programming language, Topological Data Analysis in Science and Engineering, Multiplicity (mathematics), Computational Theory and Mathematics, Laplace operator, Combinatorics, Computer Science, Physical Sciences, Chromatic scale, Independence number, Combinatorics (math.CO), Geometry and Topology, Laplacian matrix, Variational methods for eigenvalues of operators, Mathematics, Constant (computer programming)
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