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Lower bounds on the total domination number of a graph

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Abstract

A set \(S\) of vertices in a graph \(G\) is a total dominating set if every vertex of \(G\) is adjacent to a vertex in \(S\). The minimum cardinality of a total dominating set of \(G\) is the total domination number of \(G\). Much interest in total domination in graphs has arisen from a computer program Graffiti.pc that has generated several hundred conjectures on total domination (see http://cms.dt.uh.edu/faculty/delavinae/research/wowII). We prove and disprove some conjectures from Graffiti.pc concerning lower bounds on the total domination number of a graph.

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Acknowledgments

Research supported in part by the University of Johannesburg and the South African National Research Foundation.

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Correspondence to Wyatt J. Desormeaux.

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Desormeaux, W.J., Henning, M.A. Lower bounds on the total domination number of a graph. J Comb Optim 31, 52–66 (2016). https://doi.org/10.1007/s10878-014-9708-2

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  • DOI: https://doi.org/10.1007/s10878-014-9708-2

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