@article{Y. B._Hari_Chidambaram_2019, title={Total domination and vertex-edge domination in trees.}, volume={38}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3573}, abstractNote={A vertex v of a graph G = (V,E) is said to ve-dominate every edge incident to v, as well as every edge adjacent to these incident edges. A set S ⊆ V is a vertex-edge dominating set if every edge of E is ve-dominated by at least one vertex of S. The minimum cardinality of a vertex-edge dominating set of G is the vertex-edge domination number γve(G) . In this paper we prove (γt(T)−ℓ+1)/2 ≤ γve(T) ≤(γt(T)+ℓ−1)/2 and characterize trees attaining each of these bounds.}, number={2}, journal={Proyecciones (Antofagasta, On line)}, author={Y. B., Venkatakrishnan and Hari, Naresh Kumar and Chidambaram, Natarajan}, year={2019}, month={May}, pages={295-304} }