TY - JOUR
T1 - The Clique and Coclique Numbers' Bounds Based on the H-Eigenvalues of Uniform Hypergraphs
AU - Jinshan Xie & Liqun Qi
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 318
EP - 327
PY - 2015
DA - 2015/12
SN - 12
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/491.html
KW - H-eigenvalue, clique, coclique, hypergraph, tensor, signless Laplacian, Laplacian, adjacency.
AB - <p style="text-align: justify;">In this paper, some inequality relations between the Laplacian/signless Laplacian
H-eigenvalues and the clique/coclique numbers of uniform hypergraphs are presented. For a connected
uniform hypergraph, some tight lower bounds on the largest Laplacian $H^+$-eigenvalue and
signless Laplacian H-eigenvalue related to the clique/coclique numbers are given. And some upper
and lower bounds on the clique/coclique numbers related to the largest Laplacian/signless
Laplacian H-eigenvalues are obtained. Also some bounds on the sum of the largest/smallest adjacency/Laplacian/signless Laplacian H-eigenvalues of a hypergraph and its complement hypergraph
are showed. All these bounds are consistent with what we have known when $k$ is equal to 2.</p>