A constructive characterization of vertex cover Roman trees

• DOI: 10.7151/dmgt.2179
• Publication Date: 2018-11-21T16:52:54Z
• Authors: Abel Cabrera Mart...; Dorota Kuziak; González Ismael Yero
• Keywords: roman domination; vertex independence; Roman domination; outer-independent roman domination; trees; 0102 computer and information sciences; outer-independent Roman domination; 01 natural sciences; Vertex independence; vertex cover; Trees; Vertex cover; 05c69; Outer-independent Roman domination; 05c05; QA1-939; Mathematics; 05c75

A Roman dominating function on a graph G = (V (G), E (G)) is a function f : V (G) -> {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2. The Roman dominating function f is an outer-independent Roman dominating function on G if the set of vertices labeled with zero under f is an independent set. The outer-independent Roman domination number gamma(oiR) (G) is the minimum weight w(f ) = Sigma(v is an element of V), ((G)) f(v) of any outer-independent Roman dominating function f of G. A vertex cover of a graph G is a set of vertices that covers all the edges of G. The minimum cardinality of a vertex cover is denoted by alpha(G). A graph G is a vertex cover Roman graph if gamma(oiR) (G) = 2 alpha(G). A constructive characterization of the vertex cover Roman trees is given in this article.