Vol. 3, Issue 12, Part A (2017)

Abstract
A Roman dominating function on a graph G is a function f:V→{0,1,2} satisfying the condition that every vertex u∈ V for which f(u)=0 is adjacent to at least one vertex v∈ V for which f(v)=2. The weight of a roman dominating function is the value f(V)=∑_v∈V f(v). The roman domination number γ_R (G) of G is the minimum weight of a Roman dominating function on G. A Roman dominating function on G is connected roman dominating function of G if either 〈V₁∪V₂ 〉 or 〈V₂ 〉 is connected. The connected roman domination number γ_RC (G) of G is the minimum weight of a connected roman dominating function on G. A Roman dominating function on a block graph. A roman dominating function on a block graph B(G)=H is a function. The minimum weight of a roman dominating function on a block graph H is called the roman block domination number of G and is denoted by γ_RB (G). In this paper the roman domination number of block graph H and obtain some results on γ_RB (G) in terms of elements of G, but not in terms of H.