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The economic consequences of the spanish Reconquest: The long-term effects of medieval conquest and colonization [PDF]
This paper shows that a historical process that ended more than five centuries ago, the Reconquest, is very important to explain Spanish regional economic development down to the present day.
Oto-Peralias, Daniel +1 more
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Total Roman {2}-Dominating Functions in Graphs
A Roman {2}-dominating function (R2F) is a function f : V → {0, 1, 2} with the property that for every vertex v ∈ V with f(v) = 0 there is a neighbor u of v with f(u) = 2, or there are two neighbors x, y of v with f(x) = f(y) = 1.
Ahangar H. Abdollahzadeh +3 more
doaj +1 more source
Quasi-total Roman Domination in Graphs [PDF]
[EN] A quasi-total Roman dominating function on a graph G=(V,E) is a function f:V ->{0,1,2}satisfying the following: Every vertex for which u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2, and If x is an isolated vertex in ...
Cabrera García, Suitberto +2 more
core +3 more sources
Signed Total Roman Edge Domination In Graphs
Let G = (V,E) be a simple graph with vertex set V and edge set E. A signed total Roman edge dominating function of G is a function f : Ʃ → {−1, 1, 2} satisfying the conditions that (i) Ʃe′∈N(e) f(e′) ≥ 1 for each e ∈ E, where N(e) is the open ...
Asgharsharghi Leila +1 more
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Total Protection of Lexicographic Product Graphs
Given a graph G with vertex set V (G), a function f : V (G) → {0, 1, 2} is said to be a total dominating function if Σu∈N(v) f(u) > 0 for every v ∈ V (G), where N(v) denotes the open neighbourhood of v. Let Vi = {x ∈ V (G) : f(x) = i}. A total dominating
Martínez Abel Cabrera +1 more
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Total Roman domination in the lexicographic product of graphs [PDF]
A total Roman dominating function of a graph $G=(V,E)$ is a function $f: V(G)\to \{0,1,2\}$ such that for every vertex $v$ with $f(v)=0$ there exists a vertex $u$ adjacent to $v$ with $f(u)=2$, and such that the subgraph induced by the set of vertices ...
Campanelli, Nicolás, Kuziak, Dorota
core +1 more source
Halmyris (Murighiol, Tulcea County, Romania) is one of the most important Roman settlements located in the inferior sector of the Danube Delta, in the easternmost part of Scythia province during the Late Antiquity.
Margareta Simina Stanc +4 more
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Quasi total double Roman domination in graphs
A quasi total double Roman dominating function (QTDRD-function) on a graph [Formula: see text] is a function [Formula: see text] having the property that (i) if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w
S. Kosari +4 more
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On The Total Roman Domination in Trees
A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by ...
Amjadi Jafar +2 more
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Total Roman domination for proper interval graphs
A function f:V → {0,1,2} is a total Roman dominating function (TRDF) on a graph G=(V,E) if for every vertex v ∈ V with f(v) = 0 there is a vertex u adjacent to v with f(u) = 2 and for every vertex v ∈ V with f(v) > 0 there exists a vertex u ∈ NG(v ...
Abolfazl Poureidi
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