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Edge lifting and total domination in graphs

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Abstract

Let u and v be vertices of a graph G, such that the distance between u and v is two and x is a common neighbor of u and v. We define the edge lift of uv off x as the process of removing edges ux and vx while adding the edge uv to G. In this paper, we investigate the effect that edge lifting has on the total domination number of a graph. Among other results, we show that there are no trees for which every possible edge lift decreases the total domination number and that there are no trees for which every possible edge lift leaves the total domination number unchanged. Trees for which every possible edge lift increases the total domination number are characterized.

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Authors and Affiliations

  1. Department of Mathematics, University of Johannesburg, Auckland Park, 2006, South Africa

    Wyatt J. Desormeaux & Michael A. Henning

  2. Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN, 37614-0002, USA

    Teresa W. Haynes

Authors
  1. Wyatt J. Desormeaux
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  2. Teresa W. Haynes
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  3. Michael A. Henning
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Correspondence to Wyatt J. Desormeaux.

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Desormeaux, W.J., Haynes, T.W. & Henning, M.A. Edge lifting and total domination in graphs. J Comb Optim 25, 47–59 (2013). https://doi.org/10.1007/s10878-011-9416-0

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  • DOI: https://doi.org/10.1007/s10878-011-9416-0

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