Roman domination is a historically inspired variety of general domination such that every vertex is labeled with labels from {0, 1, 2}. Roman domination number is the smallest of the sums of labels fulfilling condition that every vertex, labeled 0, has a neighbor, labeled 2. Using algebraic approach we give O(C) time algorithm for computing Roman domination number of special classes of polygrap...

A subset X of edges of a graph G is called an edge dominating set of G if every edge not in X is adjacent to some edge in X . The edge domination number γ′(G) of G is the minimum cardinality taken over all edge dominating sets of G. An edge Roman dominating function of a graph G is a function f : E(G) → {0, 1, 2} such that every edge e with f(e) = 0 is adjacent to some edge e′ with f(e′) = 2. T...

A Roman dominating function on a graph G = (V, E) is a function f : V → {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 weight of a Roman dominating function is the value f(V ) = ∑ u∈V f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this pape...

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 Luther insisted on the royal, common or universal priesthood of all baptised, as Second Vatican Council also recalled, referring to mutual complementarity between and ministerial priesthood, which however differ non tantum gradu sed essentiam (cf. LG 10). These pages review main points according Luther's proposal response Council...

The purpose of this study was to compare the epidemiology of freestyle and Greco-Roman wrestling injuries sustained during a 2006 United States (US) national tournament. A prospective injury surveillance study was conducted at the US 2006 ASICS/Vaughan Cadet and Junior National Championships. There were 83 freestyle- and 55 Greco-Roman-related injuries sustained, with the rate of injury per 100...

BACKGROUND Genetic influences have been shown to play a major role in determining the risk of alcohol dependence (AD) in both women and men; however, little attention has been directed to identifying the major sources of genetic variation in AD risk. METHOD Diagnostic telephone interview data from young adult Australian twin pairs born between 1964 and 1971 were analyzed. Cox regression model...

a roman dominating function (rdf) on a graph g = (v,e) is defined to be a function 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. a set s v is a restrained dominating set if every vertex not in s is adjacent to a vertex in s and to a vertex in . we define a restrained roman dominating function on a graph g = (v,e) to be ...