Work

Paired domination in graphs with minimum degree four

Year: 2025

Type: article

Abstract: A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S admits a perfect matching. The minimum cardinality of a paired dominating set of G is the paired domination number γ pr ( G ) of G . We show that if G is a graph of order n and δ ( G ) ≥ 4 , then γ pr ( G ) ≤ 10 17 n < 0.5883 n .

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2025.114923

Authors: Csilla Bujtás, Michael A. Henning

Institutions: University of Ljubljana, Institute of Mathematics, Physics, and Mechanics, University of Johannesburg

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funders: Javna Agencija za Raziskovalno Dejavnost RS, University of Johannesburg