1Academy of Mathematics and Systems Science, Chinese Academy of Sciences 2LMAM and School of Mathematical Sciences, Peking University, Beijing, P.R. China
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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.
1
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
2
LMAM and School of Mathematical Sciences, Peking University, Beijing, P.R. China
@article{10_37236_8951,
author = {Xin Luo and Dong Zhang},
title = {Spectrum of signless {1-Laplacian} on simplicial complexes},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {2},
doi = {10.37236/8951},
zbl = {1441.05254},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8951/}
}
TY - JOUR
AU - Xin Luo
AU - Dong Zhang
TI - Spectrum of signless 1-Laplacian on simplicial complexes
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/8951/
DO - 10.37236/8951
ID - 10_37236_8951
ER -
%0 Journal Article
%A Xin Luo
%A Dong Zhang
%T Spectrum of signless 1-Laplacian on simplicial complexes
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/8951/
%R 10.37236/8951
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Xin Luo; Dong Zhang. Spectrum of signless 1-Laplacian on simplicial complexes. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/8951
