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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

On Unique Realizations of Domination Chain Parameters

Jason Hedetniemi1, Kevin James1
1Department of Mathematical Sciences Clemson University Clemson, South Carolina 29634 U.S.A.
  • Published: 30/05/2017

Abstract

The domination chain \(\iota_r(G) \leq \gamma(G) \leq \iota(G) \leq \beta_o(G) \leq \Gamma(G) \leq IR(G)\), which holds for any graph \(G\), is the subject of much research. In this paper, we consider the maximum number of edges in a graph having one of these domination chain parameters equal to \(2\) through a unique realization. We show that a specialization of the domination chain still holds in this setting.

Keywords: vertex domination, vertex independence, vertex irredundance 2010 Mathematics Subject Classification: 05C6
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Citation
Jason Hedetniemi, Kevin James. On Unique Realizations of Domination Chain Parameters[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 101. 193-211. DOI: .