Some Progress on Total Bondage in Graphs

Abstract

The total bondage number b t(G) of a graph G with no isolated vertex is the cardinality of a smallest set of edges (Formula presented) for which (1) G-E′ has no isolated vertex, and (2) (Formula presented). 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. © 2013 The Author(s).