Strong Hub Sets and Strong Hub Number of Hypergraphs

Shama Kochuthundiyil Syed; Ramakrishnan Thekkan Veetil; Divya Pookulath Madhavan

doi:doi:10.11648/j.ajam.20261401.11

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Strong Hub Sets and Strong Hub Number of Hypergraphs

Shama Kochuthundiyil Syed^*, Ramakrishnan Thekkan Veetil, Divya Pookulath Madhavan

Published in American Journal of Applied Mathematics (Volume 14, Issue 1)

Received: 29 October 2025 Accepted: 8 November 2025 Published: 15 January 2026

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Abstract

This paper introduces and investigates the concepts of strong hub sets and the strong hub number in hypergraphs, extending the notion of hub sets defined for graphs. For a hypergraph H = (V, E), a subset S ⊆ V (H) is said to be a strong hub set if, for every pair of distinct vertices u, v ∈ V (H) − S, either u and v are adjacent or there exists a strong S-hyperpath joining them. The minimum cardinality of such a set is called the strong hub number of H, denoted by h∗(H). Fundamental properties of strong hub sets are established, and relationships between the strong hub number and various hypergraph parameters such as the domination number and connectivity are explored. The effects of vertex deletion and weak deletion on h∗(H) are studied, leading to several sharp bounds and recursive characterizations. In particular, it is shown that under weak deletion of a non cut vertex, the strong hub number remains invariant, while deletion of a cut vertex reduces it according to the structure of the resulting components. Special attention is devoted to hypertrees, where structural simplicity allows a precise characterization. This characterization provides an exact formula for h∗(H) in acyclic hypergraphs and establishes the foundational link between connectivity and hub-based path structure in hypertrees.

Published in	American Journal of Applied Mathematics (Volume 14, Issue 1)
DOI	10.11648/j.ajam.20261401.11
Page(s)	1-9
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), 2026. Published by Science Publishing Group

Keywords

Strong Hub Set, Strong Hub Number, Hyperpath

References

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[7]	Matthew Walsh, The hub number of a graph, International Journal of Mathematics and computer Science., 1 (2006), 117, 124.
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[9]	K. K. Mythili, C. Nandhini, Hub parameters of Hypergraph, J. Indones. Math. Soc, 30 01 (2024), 100-109. https://doi.org/10.22342/jims.30.1.1443.100-109
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Syed, S. K., Veetil, R. T., Madhavan, D. P. (2026). Strong Hub Sets and Strong Hub Number of Hypergraphs. American Journal of Applied Mathematics, 14(1), 1-9. https://doi.org/10.11648/j.ajam.20261401.11

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ACS Style

Syed, S. K.; Veetil, R. T.; Madhavan, D. P. Strong Hub Sets and Strong Hub Number of Hypergraphs. Am. J. Appl. Math. 2026, 14(1), 1-9. doi: 10.11648/j.ajam.20261401.11

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AMA Style

Syed SK, Veetil RT, Madhavan DP. Strong Hub Sets and Strong Hub Number of Hypergraphs. Am J Appl Math. 2026;14(1):1-9. doi: 10.11648/j.ajam.20261401.11

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@article{10.11648/j.ajam.20261401.11,
  author = {Shama Kochuthundiyil Syed and Ramakrishnan Thekkan Veetil and Divya Pookulath Madhavan},
  title = {Strong Hub Sets and Strong Hub Number of Hypergraphs
},
  journal = {American Journal of Applied Mathematics},
  volume = {14},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ajam.20261401.11},
  url = {https://doi.org/10.11648/j.ajam.20261401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20261401.11},
  abstract = {This paper introduces and investigates the concepts of strong hub sets and the strong hub number in hypergraphs, extending the notion of hub sets defined for graphs. For a hypergraph H = (V, E), a subset S ⊆ V (H) is said to be a strong hub set if, for every pair of distinct vertices u, v ∈ V (H) − S, either u and v are adjacent or there exists a strong S-hyperpath joining them. The minimum cardinality of such a set is called the strong hub number of H, denoted by h∗(H). Fundamental properties of strong hub sets are established, and relationships between the strong hub number and various hypergraph parameters such as the domination number and connectivity are explored. The effects of vertex deletion and weak deletion on h∗(H) are studied, leading to several sharp bounds and recursive characterizations. In particular, it is shown that under weak deletion of a non cut vertex, the strong hub number remains invariant, while deletion of a cut vertex reduces it according to the structure of the resulting components. Special attention is devoted to hypertrees, where structural simplicity allows a precise characterization. This characterization provides an exact formula for h∗(H) in acyclic hypergraphs and establishes the foundational link between connectivity and hub-based path structure in hypertrees.
},
 year = {2026}
}

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TY  - JOUR
T1  - Strong Hub Sets and Strong Hub Number of Hypergraphs

AU  - Shama Kochuthundiyil Syed
AU  - Ramakrishnan Thekkan Veetil
AU  - Divya Pookulath Madhavan
Y1  - 2026/01/15
PY  - 2026
N1  - https://doi.org/10.11648/j.ajam.20261401.11
DO  - 10.11648/j.ajam.20261401.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20261401.11
AB  - This paper introduces and investigates the concepts of strong hub sets and the strong hub number in hypergraphs, extending the notion of hub sets defined for graphs. For a hypergraph H = (V, E), a subset S ⊆ V (H) is said to be a strong hub set if, for every pair of distinct vertices u, v ∈ V (H) − S, either u and v are adjacent or there exists a strong S-hyperpath joining them. The minimum cardinality of such a set is called the strong hub number of H, denoted by h∗(H). Fundamental properties of strong hub sets are established, and relationships between the strong hub number and various hypergraph parameters such as the domination number and connectivity are explored. The effects of vertex deletion and weak deletion on h∗(H) are studied, leading to several sharp bounds and recursive characterizations. In particular, it is shown that under weak deletion of a non cut vertex, the strong hub number remains invariant, while deletion of a cut vertex reduces it according to the structure of the resulting components. Special attention is devoted to hypertrees, where structural simplicity allows a precise characterization. This characterization provides an exact formula for h∗(H) in acyclic hypergraphs and establishes the foundational link between connectivity and hub-based path structure in hypertrees.

VL  - 14
IS  - 1
ER  -

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Author Information

Shama Kochuthundiyil Syed

Department of Mathematical Sciences, Kannur University, Kannur, Kerala, India

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Ramakrishnan Thekkan Veetil

Department of Mathematical Sciences, Kannur University, Kannur, Kerala, India

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Divya Pookulath Madhavan

Department of Mathematical Sciences, Kannur University, Kannur, Kerala, India

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APA Style

Syed, S. K., Veetil, R. T., Madhavan, D. P. (2026). Strong Hub Sets and Strong Hub Number of Hypergraphs. American Journal of Applied Mathematics, 14(1), 1-9. https://doi.org/10.11648/j.ajam.20261401.11

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ACS Style

Syed, S. K.; Veetil, R. T.; Madhavan, D. P. Strong Hub Sets and Strong Hub Number of Hypergraphs. Am. J. Appl. Math. 2026, 14(1), 1-9. doi: 10.11648/j.ajam.20261401.11

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AMA Style

Syed SK, Veetil RT, Madhavan DP. Strong Hub Sets and Strong Hub Number of Hypergraphs. Am J Appl Math. 2026;14(1):1-9. doi: 10.11648/j.ajam.20261401.11

Copy | Download

@article{10.11648/j.ajam.20261401.11,
  author = {Shama Kochuthundiyil Syed and Ramakrishnan Thekkan Veetil and Divya Pookulath Madhavan},
  title = {Strong Hub Sets and Strong Hub Number of Hypergraphs
},
  journal = {American Journal of Applied Mathematics},
  volume = {14},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ajam.20261401.11},
  url = {https://doi.org/10.11648/j.ajam.20261401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20261401.11},
  abstract = {This paper introduces and investigates the concepts of strong hub sets and the strong hub number in hypergraphs, extending the notion of hub sets defined for graphs. For a hypergraph H = (V, E), a subset S ⊆ V (H) is said to be a strong hub set if, for every pair of distinct vertices u, v ∈ V (H) − S, either u and v are adjacent or there exists a strong S-hyperpath joining them. The minimum cardinality of such a set is called the strong hub number of H, denoted by h∗(H). Fundamental properties of strong hub sets are established, and relationships between the strong hub number and various hypergraph parameters such as the domination number and connectivity are explored. The effects of vertex deletion and weak deletion on h∗(H) are studied, leading to several sharp bounds and recursive characterizations. In particular, it is shown that under weak deletion of a non cut vertex, the strong hub number remains invariant, while deletion of a cut vertex reduces it according to the structure of the resulting components. Special attention is devoted to hypertrees, where structural simplicity allows a precise characterization. This characterization provides an exact formula for h∗(H) in acyclic hypergraphs and establishes the foundational link between connectivity and hub-based path structure in hypertrees.
},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Strong Hub Sets and Strong Hub Number of Hypergraphs

AU  - Shama Kochuthundiyil Syed
AU  - Ramakrishnan Thekkan Veetil
AU  - Divya Pookulath Madhavan
Y1  - 2026/01/15
PY  - 2026
N1  - https://doi.org/10.11648/j.ajam.20261401.11
DO  - 10.11648/j.ajam.20261401.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20261401.11
AB  - This paper introduces and investigates the concepts of strong hub sets and the strong hub number in hypergraphs, extending the notion of hub sets defined for graphs. For a hypergraph H = (V, E), a subset S ⊆ V (H) is said to be a strong hub set if, for every pair of distinct vertices u, v ∈ V (H) − S, either u and v are adjacent or there exists a strong S-hyperpath joining them. The minimum cardinality of such a set is called the strong hub number of H, denoted by h∗(H). Fundamental properties of strong hub sets are established, and relationships between the strong hub number and various hypergraph parameters such as the domination number and connectivity are explored. The effects of vertex deletion and weak deletion on h∗(H) are studied, leading to several sharp bounds and recursive characterizations. In particular, it is shown that under weak deletion of a non cut vertex, the strong hub number remains invariant, while deletion of a cut vertex reduces it according to the structure of the resulting components. Special attention is devoted to hypertrees, where structural simplicity allows a precise characterization. This characterization provides an exact formula for h∗(H) in acyclic hypergraphs and establishes the foundational link between connectivity and hub-based path structure in hypertrees.

VL  - 14
IS  - 1
ER  -

Copy | Download