This paper introduces the star domination polynomial of hypergraphs as an extension of the domination polynomial in graphs. Based on the concept of star domination, we define the star domination polynomial as the generating function that counts the star dominating sets of a hypergraph according to their cardinalities. We establish several fundamental properties of this polynomial and investigate its behavior under the disjoint union of hypergraphs. Explicit formulas are obtained for the star domination polynomial of important classes of hypergraphs, including r-uniform complete hypergraphs and sunflower hypergraphs, by characterizing their star dominating sets of different cardinalities. The proposed polynomial provides an algebraic representation of the distribution of star dominating sets and offers a new tool for studying domination in hypergraphs. These results extend the theory of domination polynomials to hypergraphs and provide a foundation for further research on domination parameters, hypergraph invariants, and related combinatorial polynomials.
| Published in | International Journal of Theoretical and Applied Mathematics (Volume 12, Issue 4) |
| DOI | 10.11648/j.ijtam.20261204.11 |
| Page(s) | 74-79 |
| 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 |
Hypergraph, Domination, Domination Polynomial
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APA Style
Madhavan, D. P., Syed, S. K., Veetil, R. T. (2026). The Star Domination Polynomial in Hypergraphs. International Journal of Theoretical and Applied Mathematics, 12(4), 74-79. https://doi.org/10.11648/j.ijtam.20261204.11
ACS Style
Madhavan, D. P.; Syed, S. K.; Veetil, R. T. The Star Domination Polynomial in Hypergraphs. Int. J. Theor. Appl. Math. 2026, 12(4), 74-79. doi: 10.11648/j.ijtam.20261204.11
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Download@article{10.11648/j.ijtam.20261204.11,
author = {Divya Pookulath Madhavan and Shama Kochuthundiyil Syed and Ramakrishnan Thekkan Veetil},
title = {The Star Domination Polynomial in Hypergraphs},
journal = {International Journal of Theoretical and Applied Mathematics},
volume = {12},
number = {4},
pages = {74-79},
doi = {10.11648/j.ijtam.20261204.11},
url = {https://doi.org/10.11648/j.ijtam.20261204.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20261204.11},
abstract = {This paper introduces the star domination polynomial of hypergraphs as an extension of the domination polynomial in graphs. Based on the concept of star domination, we define the star domination polynomial as the generating function that counts the star dominating sets of a hypergraph according to their cardinalities. We establish several fundamental properties of this polynomial and investigate its behavior under the disjoint union of hypergraphs. Explicit formulas are obtained for the star domination polynomial of important classes of hypergraphs, including r-uniform complete hypergraphs and sunflower hypergraphs, by characterizing their star dominating sets of different cardinalities. The proposed polynomial provides an algebraic representation of the distribution of star dominating sets and offers a new tool for studying domination in hypergraphs. These results extend the theory of domination polynomials to hypergraphs and provide a foundation for further research on domination parameters, hypergraph invariants, and related combinatorial polynomials.},
year = {2026}
}
TY - JOUR T1 - The Star Domination Polynomial in Hypergraphs AU - Divya Pookulath Madhavan AU - Shama Kochuthundiyil Syed AU - Ramakrishnan Thekkan Veetil Y1 - 2026/08/13 PY - 2026 N1 - https://doi.org/10.11648/j.ijtam.20261204.11 DO - 10.11648/j.ijtam.20261204.11 T2 - International Journal of Theoretical and Applied Mathematics JF - International Journal of Theoretical and Applied Mathematics JO - International Journal of Theoretical and Applied Mathematics SP - 74 EP - 79 PB - Science Publishing Group SN - 2575-5080 UR - https://doi.org/10.11648/j.ijtam.20261204.11 AB - This paper introduces the star domination polynomial of hypergraphs as an extension of the domination polynomial in graphs. Based on the concept of star domination, we define the star domination polynomial as the generating function that counts the star dominating sets of a hypergraph according to their cardinalities. We establish several fundamental properties of this polynomial and investigate its behavior under the disjoint union of hypergraphs. Explicit formulas are obtained for the star domination polynomial of important classes of hypergraphs, including r-uniform complete hypergraphs and sunflower hypergraphs, by characterizing their star dominating sets of different cardinalities. The proposed polynomial provides an algebraic representation of the distribution of star dominating sets and offers a new tool for studying domination in hypergraphs. These results extend the theory of domination polynomials to hypergraphs and provide a foundation for further research on domination parameters, hypergraph invariants, and related combinatorial polynomials. VL - 12 IS - 4 ER -
Department of Mathematics, Sree Narayana College, Kannur, India
Department of Mathematics, Government Women's Polytechnic College, Kozhikode, India
Department of Mathematical sciences, Kannur University, Kerala, India
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