The total bondage numbers and efficient total dominations of vertex-transitive graphs

Fu-Tao Hu, Lu Li and Jia-Bao Liu

Applied Mathematics and Computation, 2018, vol. 332, issue C, 35-41

Abstract: The total domination number of a graph G without isolated vertices is the minimum number of vertices that dominate all vertices in G. The total bondage number of G is the minimum number of edges whose removal enlarges the total domination number. In this paper, we establish a tight lower bound for the total bondage number of a vertex-transitive graph. We also obtain upper bounds for regular graphs by investigating the relation between the total bondage number and the efficient total domination. As applications, we study the total bondage numbers for some circulant graphs and toroidal meshes by characterizing the existence of efficient total dominating sets in these graphs.

Keywords: Total dominating set; Efficient total dominating set; Total bondage number; Vertex-transitive graphs (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:332:y:2018:i:c:p:35-41

DOI: 10.1016/j.amc.2018.03.046

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