A Roman domination function on a graph G = (V,E) is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u with f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman domination function f is the value f(V (G)) = ∑ u∈V (G) f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G, denoted by...

A Roman dominating function on a graph 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 weight of a Roman dominating function is the value f(V (G)) = ∑ u∈V (G) f(u). The Roman domination number γR(G) of G is the minimum weight of a Roman dominating function on G. In this paper, we s...

The fall of the Byzantine Empire in 1453 caused the ancient Christian country of Georgia to lose its close contacts with Europe for several centuries. Having grown weak because of continuous defensive wars, in 1801 Georgia allied herself with Russia and due to strong and developed historical status in the Caucasus, as well as its central geographical location, Georgia became the political-admin...

Abstract The north-eastern French city of Nancy is one the centres Art Nouveau. It has been analysed in detail many classical reviews Nouveau, but mainly relation to decorative applied art works produced at School Art. study pays attention also architecture. architectural and artistic qualities iconic Nouveau monument Villa L. Majorelle are detail, basic data about É. André, H. Gutton, J. Horne...

The popularity of natural cement (Roman cement) in buildings from the late 19th and beginning 20th century high diversity characteristics demand research mortar binders used this period Portugal. Understanding type binder historic will help project/intervention team to make best decisions terms development compatible mortars for historical conservation purposes. Casa Barbot is one Art Nouveau e...

This year the CLASSY team participated in the update summary task and made four submissions to summarization evaluation (AESOP). Our AESOP submissions used combinations of ROUGE scores along with an update (or newness) score. We also use these new metrics, which we call Nouveau ROUGE, to help train our system and evaluate new ideas on computing update summaries. CLASSY (Clustering, Linguistics,...

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k from each other. The weight of a k-distance Roman dominating function f is the value ω(f) = ∑ v∈V f(v). The k-distance Roman domination number ...