A hypergraphs, as a generalization of a general graph, is often used as an effective tool to describe complex structures in discrete mathematics, computer science and other fields. Hypergraph theory and related parameters of hypergraph are important research topics in hypergraph theory. In particular, the problem of spectral extremum of graphs has been widely concerned. This problem originates from the problem proposed by Brualdi and Solheid in 1986. That is to find the upper and lower bounds of spectral radius of a given graph class and characterize the polar graph that reaches the upper and lower bounds. Let H be a uniform hypergraph. Let A(H) be the adjacency tensor of H. In this work, by using Perron-Frobenius theorem, Hölder’s inequality and inequality of arithmetic and geometric means, we establish some upper bounds for the maximum E-eigenvalue of a uniform hypergraph instead of the degrees of vertices and edge number of hypergraph H. In addition, we characterize the extremal hypergraphs that reach the upper bounds.
| Published in | Mathematics and Computer Science (Volume 8, Issue 2) |
| DOI | 10.11648/j.mcs.20230802.13 |
| Page(s) | 51-56 |
| 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. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Uniform Hypergraphs, Adjacency Tensor, Maximal E-Eigenvalue, Degree
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APA Style
Hongyu Zhang, Feng Fu, Caoji Yin. (2023). Some Upper Bounds of Maximum E-Eigenvalues of Uniform Hypergraphs. Mathematics and Computer Science, 8(2), 51-56. https://doi.org/10.11648/j.mcs.20230802.13
ACS Style
Hongyu Zhang; Feng Fu; Caoji Yin. Some Upper Bounds of Maximum E-Eigenvalues of Uniform Hypergraphs. Math. Comput. Sci. 2023, 8(2), 51-56. doi: 10.11648/j.mcs.20230802.13
AMA Style
Hongyu Zhang, Feng Fu, Caoji Yin. Some Upper Bounds of Maximum E-Eigenvalues of Uniform Hypergraphs. Math Comput Sci. 2023;8(2):51-56. doi: 10.11648/j.mcs.20230802.13
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Download@article{10.11648/j.mcs.20230802.13,
author = {Hongyu Zhang and Feng Fu and Caoji Yin},
title = {Some Upper Bounds of Maximum E-Eigenvalues of Uniform Hypergraphs},
journal = {Mathematics and Computer Science},
volume = {8},
number = {2},
pages = {51-56},
doi = {10.11648/j.mcs.20230802.13},
url = {https://doi.org/10.11648/j.mcs.20230802.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20230802.13},
abstract = {A hypergraphs, as a generalization of a general graph, is often used as an effective tool to describe complex structures in discrete mathematics, computer science and other fields. Hypergraph theory and related parameters of hypergraph are important research topics in hypergraph theory. In particular, the problem of spectral extremum of graphs has been widely concerned. This problem originates from the problem proposed by Brualdi and Solheid in 1986. That is to find the upper and lower bounds of spectral radius of a given graph class and characterize the polar graph that reaches the upper and lower bounds. Let H be a uniform hypergraph. Let A(H) be the adjacency tensor of H. In this work, by using Perron-Frobenius theorem, Hölder’s inequality and inequality of arithmetic and geometric means, we establish some upper bounds for the maximum E-eigenvalue of a uniform hypergraph instead of the degrees of vertices and edge number of hypergraph H. In addition, we characterize the extremal hypergraphs that reach the upper bounds.},
year = {2023}
}
TY - JOUR T1 - Some Upper Bounds of Maximum E-Eigenvalues of Uniform Hypergraphs AU - Hongyu Zhang AU - Feng Fu AU - Caoji Yin Y1 - 2023/03/28 PY - 2023 N1 - https://doi.org/10.11648/j.mcs.20230802.13 DO - 10.11648/j.mcs.20230802.13 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 51 EP - 56 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20230802.13 AB - A hypergraphs, as a generalization of a general graph, is often used as an effective tool to describe complex structures in discrete mathematics, computer science and other fields. Hypergraph theory and related parameters of hypergraph are important research topics in hypergraph theory. In particular, the problem of spectral extremum of graphs has been widely concerned. This problem originates from the problem proposed by Brualdi and Solheid in 1986. That is to find the upper and lower bounds of spectral radius of a given graph class and characterize the polar graph that reaches the upper and lower bounds. Let H be a uniform hypergraph. Let A(H) be the adjacency tensor of H. In this work, by using Perron-Frobenius theorem, Hölder’s inequality and inequality of arithmetic and geometric means, we establish some upper bounds for the maximum E-eigenvalue of a uniform hypergraph instead of the degrees of vertices and edge number of hypergraph H. In addition, we characterize the extremal hypergraphs that reach the upper bounds. VL - 8 IS - 2 ER -
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