For a $k$-uniform hypergraph $H$, we obtain some trace formulas for the Laplacian tensor of $H$, which imply that $\sum_{i=1}^nd_i^s$ ($s=1,\ldots,k$) is determined by the Laplacian spectrum of $H$, where $d_1,\ldots,d_n$ is the degree sequence of $H$. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spectral characterizations of odd-bipartite hypergraphs, and give a partial answer to a question posed by Shao et al (2014). We also give some spectral properties of power hypergraphs, and show that a conjecture posed by Hu et al (2013) holds under certain conditons.
@article{10_37236_4430,
author = {Jiang Zhou and Lizhu Sun and Wenzhe Wang and Changjiang Bu},
title = {Some spectral properties of uniform hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {4},
doi = {10.37236/4430},
zbl = {1302.05114},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4430/}
}
TY - JOUR
AU - Jiang Zhou
AU - Lizhu Sun
AU - Wenzhe Wang
AU - Changjiang Bu
TI - Some spectral properties of uniform hypergraphs
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/4430/
DO - 10.37236/4430
ID - 10_37236_4430
ER -
%0 Journal Article
%A Jiang Zhou
%A Lizhu Sun
%A Wenzhe Wang
%A Changjiang Bu
%T Some spectral properties of uniform hypergraphs
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/4430/
%R 10.37236/4430
%F 10_37236_4430
Jiang Zhou; Lizhu Sun; Wenzhe Wang; Changjiang Bu. Some spectral properties of uniform hypergraphs. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/4430
