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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Graphs and Their Complements With Equal Total Domination Numbers

Wyatt J. Desormeaux1, Teresa W. Haynes2, Lucas van der Merwe3
1Department of Mathematics, University of Johannesburg, Auckland Park, 2006, South Africa
2Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614-0002 USA
3Department of Mathematics, University of Tennessee Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403, USA
  • Published: 28/02/2013

Abstract

A set \( S \) of vertices in a graph \( G \) is a total dominating set of \( G \) if every vertex of \( G \) is adjacent to some vertex in \( S \). The minimum cardinality of a total dominating set of \( G \) is the total domination number of \( G \). We study graphs having the same total domination number as their complements. In particular, we characterize the cubic graphs having this property. Also, we characterize such graphs with total domination numbers equal to two or three, and we determine properties of the ones with larger total domination numbers.

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Citation
Wyatt J. Desormeaux, Teresa W. Haynes, Lucas van der Merwe. Graphs and Their Complements With Equal Total Domination Numbers[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 087. 321-333. DOI: .