The spectral theory of graphs and hypergraphs is an active and important research field in graph and hypergraph theory. And it has extensive applications in the fields of computer science, communication networks, information science, statistical mechanics and quantum chemistry, etc. The H-eigenvalues of a hypergraph are its H-eigenvalues of adjacent tensor. This paper presents some upper and lower bounds on the largest H-eigenvalue of r-hypergraphs.
| Published in | International Journal of Discrete Mathematics (Volume 2, Issue 4) |
| DOI | 10.11648/j.dmath.20170204.13 |
| Page(s) | 132-135 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
H-eigenvalue, Hypergraph, Adjacency Tensor, Bounds
| [1] | N. L. Biggs, Algebraic Graph Theory (2nd ed.), Cambridge University Press, Cambridge, 1993. |
| [2] | F. R. K. Chung, Spectral Graph Theory, Regional Conference Series in Mathematics 92, Amer. Math. Soc., 1997. |
| [3] | J. Cooper, A. Dutle, Spectra of uniform hypergraphs, Linear Algebra Appl., 436(2012)3268-3292. |
| [4] | D. M. Cvetković, M. Doob and H. Sachs, Spectra of Graphs, Theory and Application, Academic Press, 1980. |
| [5] | K. Feng, W. Li, Spectra of hypergraphs and applications, J. Number Theory, 60(1996) no. 1, 1-22. |
| [6] | S. Hu, L. Qi, Algebraic connectivity of an even uniform hypergraph, J. Comb. Optim, 24(2011) 564-579. |
| [7] | S. Hu, L. Qi, The eigenvectors of the zero laplacian and signless laplacian eigenvalues of a uniform hypergraph, Discrete Appl Math, 169(2014) 140–151. |
| [8] | L. Qi, Eigenvalues of a real supersymmetric tensor, J. Symb. Compute., 40 (2005) 1302-1324. |
| [9] | L. Zhang, L. Qi, Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor, Numerical Linear Algebra with Applications, 19 (2012) 830-841. |
| [10] | L. Qi, Symmetric nonnegative tensors and coposotive tensors, Linear Algebra Appl., 439(2013)228-238. |
| [11] | S. Hu, L. Qi, J. Xie, The largest Laplacian and Signless Laplacian H-Eigenvalues of a Uniform Hypergraph, Linear Algebra Appl., 469(2015) 1–27. |
| [12] | J. Y. Shao, A general product of tensors with applications, Linear Algebra Appl., 439(2013)2350-2366. |
| [13] | G. Yi, Properties of spectrum of tensors on uniform hypergraphs, Master thesis of Fuzhou university, 2014. |
| [14] | J. Xie, L. Qi, Spectral directed hypergraph theoy via tensors, Linear and Multilinear Algebra, 64 (2016) 780-794. |
| [15] | C. Xu, Z. Luo, L. Qi and Z. Chen, {0, 1} Completely Positive Tensors and Multi-Hypergraphs, Linear Algebra Appl., 510 (2016) 110-123. |
APA Style
Bo Deng, Xia Wang, Chunxia Wang, Xianya Geng. (2017). Some Bounds of the Largest H-eigenvalue of R-uniform Hypergraphs. International Journal of Discrete Mathematics, 2(4), 132-135. https://doi.org/10.11648/j.dmath.20170204.13
ACS Style
Bo Deng; Xia Wang; Chunxia Wang; Xianya Geng. Some Bounds of the Largest H-eigenvalue of R-uniform Hypergraphs. Int. J. Discrete Math. 2017, 2(4), 132-135. doi: 10.11648/j.dmath.20170204.13
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Download@article{10.11648/j.dmath.20170204.13,
author = {Bo Deng and Xia Wang and Chunxia Wang and Xianya Geng},
title = {Some Bounds of the Largest H-eigenvalue of R-uniform Hypergraphs},
journal = {International Journal of Discrete Mathematics},
volume = {2},
number = {4},
pages = {132-135},
doi = {10.11648/j.dmath.20170204.13},
url = {https://doi.org/10.11648/j.dmath.20170204.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170204.13},
abstract = {The spectral theory of graphs and hypergraphs is an active and important research field in graph and hypergraph theory. And it has extensive applications in the fields of computer science, communication networks, information science, statistical mechanics and quantum chemistry, etc. The H-eigenvalues of a hypergraph are its H-eigenvalues of adjacent tensor. This paper presents some upper and lower bounds on the largest H-eigenvalue of r-hypergraphs.},
year = {2017}
}
TY - JOUR T1 - Some Bounds of the Largest H-eigenvalue of R-uniform Hypergraphs AU - Bo Deng AU - Xia Wang AU - Chunxia Wang AU - Xianya Geng Y1 - 2017/11/06 PY - 2017 N1 - https://doi.org/10.11648/j.dmath.20170204.13 DO - 10.11648/j.dmath.20170204.13 T2 - International Journal of Discrete Mathematics JF - International Journal of Discrete Mathematics JO - International Journal of Discrete Mathematics SP - 132 EP - 135 PB - Science Publishing Group SN - 2578-9252 UR - https://doi.org/10.11648/j.dmath.20170204.13 AB - The spectral theory of graphs and hypergraphs is an active and important research field in graph and hypergraph theory. And it has extensive applications in the fields of computer science, communication networks, information science, statistical mechanics and quantum chemistry, etc. The H-eigenvalues of a hypergraph are its H-eigenvalues of adjacent tensor. This paper presents some upper and lower bounds on the largest H-eigenvalue of r-hypergraphs. VL - 2 IS - 4 ER -
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