TY - JOUR T1 - The Clique and Coclique Numbers' Bounds Based on the H-Eigenvalues of Uniform Hypergraphs 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 -

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.