Trees with vertex-edge Roman Domination number twice the domination number minus one
Author
Naresh Kumar, H.
Venkatakrishnan, Y. B.
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/356210.22199/issn.0717-6279-2020-06-0084
Abstract
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 ∈ E or wv ∈ 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 veR(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.