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Volume 12, Issue 2
The Clique and Coclique Numbers' Bounds Based on the H-Eigenvalues of Uniform Hypergraphs

Jinshan Xie & Liqun Qi

Int. J. Numer. Anal. Mod., 12 (2015), pp. 318-327.

Published online: 2015-12

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  • Abstract

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.

  • Keywords

H-eigenvalue, clique, coclique, hypergraph, tensor, signless Laplacian, Laplacian, adjacency.

  • AMS Subject Headings

05C65, 15A18

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-318, author = {Jinshan Xie and Liqun Qi}, title = {The Clique and Coclique Numbers' Bounds Based on the H-Eigenvalues of Uniform Hypergraphs}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {2}, pages = {318--327}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/491.html} }
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 -

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.

Jinshan Xie and Liqun Qi. (2015). The Clique and Coclique Numbers' Bounds Based on the H-Eigenvalues of Uniform Hypergraphs. International Journal of Numerical Analysis and Modeling. 12 (2). 318-327. doi:
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