TY - JOUR AU - Y. B., Venkatakrishnan AU - Hari, Naresh Kumar AU - Chidambaram, Natarajan PY - 2019/05/30 Y2 - 2024/03/29 TI - Total domination and vertex-edge domination in trees. JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 38 IS - 2 SE - DO - UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3573 SP - 295-304 AB - 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. ER -