Network Reliability Parameters

Abstract

Let G=(V,E)G=(V,E) be a finite undirected graph with no isolated vertices. A set SVS \subseteq V is said to be a total dominating set of GG if every vertex in VV is adjacent to some vertex in SS. The total domination number, γt(G)\gamma_{t}(G), is the minimum cardinality of a total dominating set in GG. We define the kk-total bondage to be the minimum number of edges to remove from GG so that the resulting graph has a total dominating number at least kk more than γt(G)\gamma_{t}(G). In this work we establish general properties of kk-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

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