Research Article
The Star Domination Polynomial in Hypergraphs
Issue:
Volume 12, Issue 4, August 2026
Pages:
74-79
Received:
26 June 2026
Accepted:
8 July 2026
Published:
13 August 2026
DOI:
10.11648/j.ijtam.20261204.11
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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.
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 fundament...
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,
Shama Kochuthundiyil Syed
