When we examine the stories of women leaders in the early church—especially the stories of their actions for alleviating suffering—their teaching on the causes of suffering comes into focus: ignorance and fear which are the root of alienation, isolation, and divisions among people and from the earth. Ignorance and fear also manifest in patterns of social injustice and in organized systems of op...

In a graph G, a vertex dominates itself and its neighbors. A subset S of V is called a dominating set in G if every vertex in V-S is adjacent to at least one vertex in S. The minimum cardinality taken over all, the minimal double dominating set which is called Fuzzy Double Domination Number and which is denoted as ) (G fdd  . A set V S  is called a Triple dominating set of a graph G if every ...

For a graph G=(V,E) with V=V(G) and E=E(G), perfect double Italian dominating function is f:V→{0,1,2,3} having the property that 3≤∑u∈NG[v]f(u)≤4, for every vertex v∈G f(v)∈{0,1}. The weight of f sum f(V)=∑v∈V(G)f(v) minimum on G domination number γdIp(G) G. We initiate study functions. check γdIp some standard graphs evaluate γdI such graphs. functions versus Roman are perused. NP-completeness...

In a graph G=(V,E), where every vertex is assigned 0, 1 or 2, f an assignment such that 0 has at least one neighbor 2 and all vertices labeled by are independent, then called outer independent Roman dominating function (OIRDF). The domination strengthened if 1, 3, each two neighbors double (OIDRDF). weight of (OIDRDF) OIRDF the sum f(v) for v?V. (double) number (?oidR(G)) ?oiR(G) minimum taken ...

The k-tuple domination problem, for a fixed positive integer k, is to find a minimum size vertex subset such that every vertex in the graph is dominated by at least k vertices in this set. The case when k 2 is called 2-tuple domination problem or double domination problem. In this paper, the 2-tuple domination problem is studied on interval graphs from an algorithmic point of view, which takes ...