Partial Total Domination in Hypergraphs

Abdulkafi Sanad () and Chaoqian Li
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Abdulkafi Sanad: School of Mathematics and Statistics, Yunnan University, Kunming 650106, China
Chaoqian Li: School of Mathematics and Statistics, Yunnan University, Kunming 650106, China

Mathematics, 2025, vol. 13, issue 6, 1-9

Abstract: This paper establishes fundamental results for partial total domination in hypergraphs. We present tight bounds for the partial total domination number in k -uniform hypergraphs, demonstrate relationships with classical domination parameters, and provide constructive proofs using hypergraph transformation techniques. Applications in sensor networks and biological systems are discussed with supporting examples. Key results include a general upper bound of k k − 1 γ ( H ) for k -uniform hypergraphs without isolated vertices, verified through both analytic methods and computational examples.

Keywords: partial domination; partial total domination; F -isolation set; hypergraphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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