Some Progress on Total Bondage in Graphs
Nader Jafari Rad, Joanna Raczek · Graphs and Combinatorics · 2013
The total bondage number b t (G) of a graph G with no isolated vertex is the cardinality of a smallest set of edges $${E^{\prime}\subseteq E(G)}$$ for which (1) G−E′ has no isolated vertex, and (2) $${\gamma_{t}(G-E^{\prime})>\gamma_{t}(G)}$$ . We improve some results on the total bondage number of a graph and give a constructive characterization of a certain class of trees achieving the upper bound on the total bondage number.