Roman Edge Semi-Total Block Domination of a Graph,
Girish V.R., P. Usha · Asia Pacific Journal of Mathematics · 2018
A graph G = (V, E), semi-total block graph T b (G) = H, whose set of vertices is the union of the set of vertices and blocks of G in whose two vertices are adjacent if and only if the corresponding vertices of G are adjacent or the corresponding members are incident.A Roman edge dominating function of a graph G = (V, E) is a function f : E → {0, 1, 2} satisfying the condition for which f (e) = 0 is adjacent to atleast to one edge h for which f (h) = 2.The weight of a roman edge dominating function is the value of f (E) = e∈E f (e).The Roman edge domination number of a graph G denoted by γ re (G), equals the minimum weight of a roman edge dominating function of G.A roman edge dominating function of a graph H is a roman semi-total block dominating function if g : w → {0, 1, 2} satisfying the condition for which g(e) = 0 is adjacent to atleast to one edge h for which g(h) = 2.The weight of a roman edge semi-total block dominating function is the value of g(w) = e∈w g(e).The Roman edge semi-total block domination number of a graph G denoted by γ re (T b (G)), equals the minimum weight of a roman edge semi-total block dominating function of G.In this paper we study the graph theoretic properties of this variant of the domination number H = T b (G) and obtained many bounds of it in terms of its original graph G. 2010 Mathematics Subject Classification.05C69.