Opuscula Math. 28, no. 3 (2008), 331-334

Opuscula Mathematica

On equality in an upper bound for the acyclic domination number

Vladimir Samodivkin

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.

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  • Vladimir Samodivkin
  • University of Architecture Civil Engineering and Geodesy, Department of Mathematics, Hristo Smirnenski 1 Blv., 1046 Sofia, Bulgaria
  • Received: 2007-06-11.
  • Accepted: 2008-01-15.
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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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