Edge lifting and total domination in graphs

Wyatt J. Desormeaux (), Teresa W. Haynes () and Michael A. Henning ()
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Wyatt J. Desormeaux: University of Johannesburg
Teresa W. Haynes: East Tennessee State University
Michael A. Henning: University of Johannesburg

Journal of Combinatorial Optimization, 2013, vol. 25, issue 1, No 3, 47-59

Abstract: 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.

Keywords: Edge lifting; Edge splitting; Total domination (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-011-9416-0

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