The $k$-Total Bondage Number of a Graph

Authors

• Jean-Pierre Appel, Drexel UniversityFollow
• Gabrielle Fischberg, Tufts UniversityFollow
• Kyle Kelley, Kenyon CollegeFollow
• Nathan B. Shank, Moravian UniversityFollow
• Eliel Sosis, University of MichiganFollow

Abstract

Let \(G=(V,E)\) be a connected, finite undirected graph. A set \(S \subseteq V\) is said to be a total dominating set of \(G\) if every vertex in \(V\) is adjacent to some vertex in \(S\). The total domination number, \(\gamma_{t}(G)\), is the minimum cardinality of a total dominating set in \(G\). We define the \(k\)-total bondage of $G$ to be the minimum number of edges to remove from \(G\) so that the resulting graph has a total domination number at least \(k\) more than \(\gamma_{t}(G)\). In this work we establish general properties of \(k\)-total bondage and find exact values for certain graph classes including paths, cycles, wheels, complete and complete bipartite graphs.

Recommended Citation

Appel, Jean-Pierre; Fischberg, Gabrielle; Kelley, Kyle; Shank, Nathan B.; and Sosis, Eliel (2026) "The $k$-Total Bondage Number of a Graph," Theory & Applications of Graphs: Vol. 13: Iss. 1, Article 3.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol13/iss1/3