Trees with vertex-edge Roman Domination number twice the domination number minus one

• Naresh Kumar, H. ^[1] ; Venkatakrishnan, Y. B. ^[1]
  1. [1] SASTRA University

     SASTRA University

     India

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 6, 2020, págs. 1381-1392
• Idioma: inglés
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• Resumen

  • 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 ?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.