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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Ramakrishnan, T.V.
Department of Mathematics, Kannur University, Kannur, Kerala
Electrical & Electronics Engineering

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A new look at the concept of domination in hypergraphs Divya, P.M.; Ramakrishnan, T.V.; Arumugam, Subramanian
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.2.3

Abstract

In this paper we propose a new definition of domination in hypergraphs in such a way that when restricted to graphs it is the usual domination in graphs. Let H = (V,E) be a hypergraph. A subset S of V is called a dominating set of H if for every vertex v in V -S, there exists an edge e ∈ E such that v ∈ e and e-{v}⊆ S. The minimum cardinality of a dominating set of H is called the domination number of H and is denoted by γ(H). We determine the domination number for several classes of uniform hypergraphs. We characterise minimal dominating sets and introduce the concept of independence and irredundance leading to domination chain in hypergraphs.
Co-Authors Arumugam, Subramanian Divya, P.M.