Abstract
Let G=(V,E) be a finite undirected graph with no isolated vertices. A set S⊆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, γt(G), is the minimum cardinality of a total dominating set in G. We define the k-total bondage to be the minimum number of edges to remove from G so that the resulting graph has a total dominating number at least k more than γt(G). In this work we establish general properties of k-total bondage, exact values for certain graph classes including paths, cycles, and wheels, and obtain upper bounds for complete and complete bipartite graphs.
- Peer Researchers
- Gabriel Fischberg
- Kyle Kelley
- Eliel Sosis
- Mentors
- Dr. Nathan Shank