@article{Naresh Kumar_Venkatakrishnan_2020, title={Trees with vertex-edge Roman Domination number twice the domination number minus one}, volume={39}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3562}, DOI={10.22199/issn.0717-6279-2020-06-0084}, abstractNote={<p><em>A vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V, E) is a function f : V (G) → {0, 1, 2} such that for each edge e = uv either max{f (u), f (v)} ≠ 0 or there exists a vertex w such that either wu </em>∈<em> E or wv </em>∈<em> E and f (w) = 2. The weight  of a ve-RDF is the sum of its function values over all vertices. The vertex-edge Roman domination number of a graph G, denoted by γ <sub>veR</sub>(G), is the minimum weight of a ve-RDF G. We characterize trees with vertexedge roman domination number equal to twice domination number minus one.</em></p>}, number={6}, journal={Proyecciones (Antofagasta, On line)}, author={Naresh Kumar, H. and Venkatakrishnan, Y. B.}, year={2020}, month={Nov.}, pages={1381-1392} }