Some Progress on Total Bondage in Graphs |
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| Authors: | Nader Jafari Rad Joanna Raczek |
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| Institution: | 1. Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
2. Department of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, Gdańsk, 80-233, Poland
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| 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 ${E^{\prime}\subseteq E(G)}$ 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. |
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