Vertex covers and secure domination in graphs

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dc.contributor.authorBurger A.P.
dc.contributor.authorHenning M.A.
dc.contributor.authorVan Vuuren J.H.
dc.date.accessioned2011-05-15T16:05:22Z
dc.date.available2011-05-15T16:05:22Z
dc.date.issued2008
dc.description.abstractLet G = (V, E) be a graph and let S ⊆ V. The set S is a dominating set of G if every vertex in V \ S is adjacent to some vertex in S. The set S is a secure dominating set of G if for each u ∈V \ S, there exists a vertex v ∈ S such that uv ∈ E and (S \ {v}) ∪ {u}is a dominating set of G. The minimum cardinality of a secure dominating set in G is the secure domination number γs(G) of G. We show that if G is a connected graph of order n with minimum degree at least two that is not a 5-cycle, then γs (G) ≤ n/2 and this bound is sharp. Our proof uses a covering of a subset of V(G) by vertex-disjoint copies of subgraphs each of which is isomorphic to K2 or to an odd cycle. © 2008 NISC Pty Ltd.
dc.description.versionArticle
dc.identifier.citationQuaestiones Mathematicae
dc.identifier.citation31
dc.identifier.citation2
dc.identifier.issn16073606
dc.identifier.other10.2989/QM.2008.31.2.5.477
dc.identifier.urihttp://hdl.handle.net/10019.1/13100
dc.titleVertex covers and secure domination in graphs
dc.typeArticle
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