Opuscula Mathematica

Opuscula Math.
 28
, no. 3
 (), 331-334
Opuscula Mathematica

On equality in an upper bound for the acyclic domination number


Abstract. A subset \(A\) of vertices in a graph \(G\) is acyclic if the subgraph it induces contains no cycles. The acyclic domination number \(\gamma_a(G)\) of a graph \(G\) is the minimum cardinality of an acyclic dominating set of \(G\). For any graph \(G\) with \(n\) vertices and maximum degree \(\Delta(G)\), \(\gamma_a(G) \leq n - \Delta(G)\). In this paper we characterize the connected graphs and the connected triangle-free graphs which achieve this upper bound.
Keywords: dominating set, acyclic set, independent set, acyclic domination number.
Mathematics Subject Classification: 05C69.
Cite this article as:
Vladimir Samodivkin, On equality in an upper bound for the acyclic domination number, Opuscula Math. 28, no. 3 (2008), 331-334
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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