Relevant bibliographies by topics / Roman domination

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Academic literature on the topic 'Roman domination'

Author: Grafiati
Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "Roman domination"

1

KUMAR, H. NARESH, and Y. B. VENKATAKRISHNAN. "Vertex-Edge Roman Domination." Kragujevac Journal of Mathematics 45, no. 5 (2021): 685–98. http://dx.doi.org/10.46793/kgjmat2105.685k.

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A vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V,E) is a function f : V (G) →{0, 1, 2} such that for each edge e = uv either max{f(u),f(v)}≠0 or there exists a vertex w such that either wu ∈ E or wv ∈ E and f(w) = 2. The weight of a ve-RDF is the sum of its function values over all vertices. The vertex-edge Roman domination number of a graph G, denoted by γveR(G), is the minimum weight of a ve-RDF G. In this paper, we initiate a study of vertex-edge Roman dominaton. We first show that determining the number γveR(G) is NP-complete even for bipartite graphs. Then we show that if T is a tree different from a star with order n, l leaves and s support vertices, then γveR(T) ≥ (n − l − s + 3)∕2, and we characterize the trees attaining this lower bound. Finally, we provide a characterization of all trees with γveR(T) = 2γ′(T), where γ′(T) is the edge domination number of T.
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Entero, Giovannie, and Stephanie Espinola. "On the Global Distance Roman Domination of Some Graphs." European Journal of Pure and Applied Mathematics 16, no. 1 (January 29, 2023): 44–61. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4478.

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Let k ∈ Z +. A k − distance Roman dominating function (kDRDF) on G = (V, E) is a function f : V → {0, 1, 2} such that for every vertex v with f(v) = 0, there is a vertex u with f(u) = 2 with d(u, v) ≤ k. The function f is a global k − distance Roman dominating function (GkDRDF) on G if and only if f is a k − distance Roman dominating function (kDRDF) on G and on its complement G. The weight of the global k − distance Roman dominating function (GkDRDF) f is the value w(f) = P x∈V f(x). The minimum weight of the global k − distance Roman dominating function (GkDRDF) on the graph G is called the global k − distance Roman domination number of G and is denoted as γ k gR(G). A γ k gR(G) − function is the global k − distance Roman dominating function on G with weight γ k gR(G). Note that, the global 1 − distance Roman domination number γ 1 gR(G) is the usual global Roman domination number γgR(G), that is, γ 1 gR(G) = γgR(G). The authors initiated this study. In this paper, the authors obtained and established the following results: preliminary results on global distance Roman domination; the global distance Roman domination on Kn, Kn, Pn, and Cn; and, some bounds and characterizations of global distance Roman domination over any graphs.
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Li, Yong, Qiong Li, Jian He, Xinruan Fan, and Zhaoheng Ding. "On the Unique Response Roman Domination Numbers of Graphs." Journal of Computational and Theoretical Nanoscience 13, no. 10 (October 1, 2016): 7362–65. http://dx.doi.org/10.1166/jctn.2016.5727.

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Let G be a graph with vertex set V(G). A function f: V(G) → {0, 1, 2} with the ordered partition (V0, V1, V2) of V(G), where Vi = {V∈V(G) | f(V) = i} for i = 0, 1, 2, is a Roman dominating function if x ∈ V0 implies |N(x)∩V2|≥ 1. It is a unique response Roman function if x ∈ V0 implies |N(x) ≥ V2|≤ 1 and x ∈ V1 ∪ V2 implies that |N(x) ∩ V2| = 0. A function f: V(G) → {0, 1, 2} is a unique response Roman dominating function if it is both a unique response Roman function and a Roman dominating function. The unique response Roman domination number, denoted by uR(G), of G is the minimum weight of a unique response Roman dominating function. In this paper we study the unique response Roman domination of graphs, and provide some graphs whose unique response Roman domination number equals to the independent Roman domination number.
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Chellali, Mustapha, Teresa Haynes, and Stephen Hedetniemi. "Lower bounds on the Roman and independent Roman domination numbers." Applicable Analysis and Discrete Mathematics 10, no. 1 (2016): 65–72. http://dx.doi.org/10.2298/aadm151112023c.

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A Roman dominating function (RDF) on a graph G 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 of G for which f(v) = 2. The weight of a Roman dominating function is the sum f(V) = ?v?V f(v), and the minimum weight of a Roman dominating function f is the Roman domination number ?R(G). An RDF f is called an independent Roman dominating function (IRDF) if the set of vertices assigned positive values under f is independent. The independent Roman domination number iR(G) is the minimum weight of an IRDF on G. We show that for every nontrivial connected graph G with maximum degree ?, ?R(G)? ?+1/??(G) and iR(G) ? i(G) + ?(G)/?, where ?(G) and i(G) are, respectively, the domination and independent domination numbers of G. Moreover, we characterize the connected graphs attaining each lower bound. We give an additional lower bound for ?R(G) and compare our two new bounds on ?R(G) with some known lower bounds.
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Amjadi, J., S. Nazari-Moghaddam, and S. M. Sheikholeslami. "Global total Roman domination in graphs." Discrete Mathematics, Algorithms and Applications 09, no. 04 (August 2017): 1750050. http://dx.doi.org/10.1142/s1793830917500501.

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A total Roman dominating function (TRDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the conditions (i) every vertex [Formula: see text] for which [Formula: see text] is adjacent at least one vertex [Formula: see text] for which [Formula: see text] and (ii) the subgraph of [Formula: see text] induced by the set of all vertices of positive weight has no isolated vertex. The weight of a TRDF is the sum of its function values over all vertices. A total Roman dominating function [Formula: see text] is called a global total Roman dominating function (GTRDF) if [Formula: see text] is also a TRDF of the complement [Formula: see text] of [Formula: see text]. The global total Roman domination number of [Formula: see text] is the minimum weight of a GTRDF on [Formula: see text]. In this paper, we initiate the study of global total Roman domination number and investigate its basic properties. In particular, we relate the global total Roman domination and the total Roman domination and the global Roman domination number.
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Shao, Zehui, Doost Ali Mojdeh, and Lutz Volkmann. "Total Roman {3}-domination in Graphs." Symmetry 12, no. 2 (February 9, 2020): 268. http://dx.doi.org/10.3390/sym12020268.

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For a graph G = ( V , E ) with vertex set V = V ( G ) and edge set E = E ( G ) , a Roman { 3 } -dominating function (R { 3 } -DF) is a function f : V ( G ) → { 0 , 1 , 2 , 3 } having the property that ∑ u ∈ N G ( v ) f ( u ) ≥ 3 , if f ( v ) = 0 , and ∑ u ∈ N G ( v ) f ( u ) ≥ 2 , if f ( v ) = 1 for any vertex v ∈ V ( G ) . The weight of a Roman { 3 } -dominating function f is the sum f ( V ) = ∑ v ∈ V ( G ) f ( v ) and the minimum weight of a Roman { 3 } -dominating function on G is the Roman { 3 } -domination number of G, denoted by γ { R 3 } ( G ) . Let G be a graph with no isolated vertices. The total Roman { 3 } -dominating function on G is an R { 3 } -DF f on G with the additional property that every vertex v ∈ V with f ( v ) ≠ 0 has a neighbor w with f ( w ) ≠ 0 . The minimum weight of a total Roman { 3 } -dominating function on G, is called the total Roman { 3 } -domination number denoted by γ t { R 3 } ( G ) . We initiate the study of total Roman { 3 } -domination and show its relationship to other domination parameters. We present an upper bound on the total Roman { 3 } -domination number of a connected graph G in terms of the order of G and characterize the graphs attaining this bound. Finally, we investigate the complexity of total Roman { 3 } -domination for bipartite graphs.
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Martínez, Abel Cabrera, Iztok Peterin, and Ismael G. Yero. "Roman domination in direct product graphs and rooted product graphs." AIMS Mathematics 6, no. 10 (2021): 11084–96. http://dx.doi.org/10.3934/math.2021643.

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<abstract><p>Let $ G $ be a graph with vertex set $ V(G) $. A function $ f:V(G)\rightarrow \{0, 1, 2\} $ is a Roman dominating function on $ G $ if every vertex $ v\in V(G) $ for which $ f(v) = 0 $ is adjacent to at least one vertex $ u\in V(G) $ such that $ f(u) = 2 $. The Roman domination number of $ G $ is the minimum weight $ \omega(f) = \sum_{x\in V(G)}f(x) $ among all Roman dominating functions $ f $ on $ G $. In this article we study the Roman domination number of direct product graphs and rooted product graphs. Specifically, we give several tight lower and upper bounds for the Roman domination number of direct product graphs involving some parameters of the factors, which include the domination, (total) Roman domination, and packing numbers among others. On the other hand, we prove that the Roman domination number of rooted product graphs can attain only three possible values, which depend on the order, the domination number, and the Roman domination number of the factors in the product. In addition, theoretical characterizations of the classes of rooted product graphs achieving each of these three possible values are given.</p></abstract>
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Chellali, Mustapha, and Nader Jafari Rad. "Trees with independent Roman domination number twice the independent domination number." Discrete Mathematics, Algorithms and Applications 07, no. 04 (December 2015): 1550048. http://dx.doi.org/10.1142/s1793830915500482.

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A Roman dominating function (RDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula: see text] for which [Formula: see text] is adjacent to at least one vertex [Formula: see text] for which [Formula: see text]. The weight of a RDF [Formula: see text] is the value [Formula: see text]. The Roman domination number, [Formula: see text], of [Formula: see text] is the minimum weight of a RDF on [Formula: see text]. An RDF [Formula: see text] is called an independent Roman dominating function (IRDF) if the set [Formula: see text] is an independent set. The independent Roman domination number, [Formula: see text], is the minimum weight of an IRDF on [Formula: see text]. In this paper, we study trees with independent Roman domination number twice their independent domination number, answering an open question.
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González, Yero, and Juan Rodríguez-Velázquez. "Roman domination in Cartesian product graphs and strong product graphs." Applicable Analysis and Discrete Mathematics 7, no. 2 (2013): 262–74. http://dx.doi.org/10.2298/aadm130813017g.

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A map f : V ? {0, 1, 2} is a Roman dominating function for G if for every vertex v with f(v) = 0, there exists a vertex u, adjacent to v, with f(u) = 2. The weight of a Roman dominating function is f(V ) = ?u?v f(u). The minimum weight of a Roman dominating function on G is the Roman domination number of G. In this article we study the Roman domination number of Cartesian product graphs and strong product graphs.
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Paleta, Leonard Mijares, and Ferdinand Paler Jamil. "More on Perfect Roman Domination in Graphs." European Journal of Pure and Applied Mathematics 13, no. 3 (July 31, 2020): 529–48. http://dx.doi.org/10.29020/nybg.ejpam.v13i3.3763.

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A perfect Roman dominating function on a graph G = (V (G), E(G)) is a function f : V (G) → {0, 1, 2} for which each u ∈ V (G) with f(u) = 0 is adjacent to exactly one vertex v ∈ V (G) with f(v) = 2. The weight of a perfect Roman dominating function f is the value ωG(f) = Pv∈V (G) f(v). The perfect Roman domination number of G is the minimum weight of a perfect Roman dominating function on G. In this paper, we study the perfect Roman domination numbers of graphs under some binary operation
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Dissertations / Theses on the topic "Roman domination"

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Carney, Nicholas. "Roman Domination Cover Rubbling." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etd/3617.

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In this thesis, we introduce Roman domination cover rubbling as an extension of domination cover rubbling. We define a parameter on a graph $G$ called the \textit{Roman domination cover rubbling number}, denoted $\rho_{R}(G)$, as the smallest number of pebbles, so that from any initial configuration of those pebbles on $G$, it is possible to obtain a configuration which is Roman dominating after some sequence of pebbling and rubbling moves. We begin by characterizing graphs $G$ having small $\rho_{R}(G)$ value. Among other things, we also obtain the Roman domination cover rubbling number for paths and give an upper bound for the Roman domination cover rubbling number of a tree.
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Alhashim, Alawi I. "Roman Domination in Complementary Prisms." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3175.

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The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect match- ing between the corresponding vertices of G and G. A Roman dominating function on a graph G = (V,E) is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 is adjacent to a vertex with label 2. The Roman domination number γR(G) of G is the minimum f(V ) = Σv∈V f(v) over all such functions of G. We study the Roman domination number of complementary prisms. Our main results show that γR(GG) takes on a limited number of values in terms of the domination number of GG and the Roman domination numbers of G and G.
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Egunjobi, Ayotunde. "Perfect Double Roman Domination of Trees." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etd/3576.

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Curro', Vincenzo. "The Roman Domination Problem on Grid Graphs." Doctoral thesis, Università di Catania, 2014. http://hdl.handle.net/10761/1561.

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Domination is a rapidly developing area of research in graph theory. This dissertation focuses on the Roman Domination Problem; it was introduced quite recently and has some interesting applications in real world problems such military strategies and wireless networking. Given a graph, a Roman Dominating Function is a function that labels the vertices of the graph with an integer between 0, 1, 2, satisfying the condition that every vertex labeled by 0 is adjacent to at least one vertex labeled by 2. The weight of a Roman Dominating Function is the sum of all the labels, and the minimum weight is called the Roman Domination Number. The Roman Domination Problem is to find such number and function. In this dissertation we study the Roman Domination Problem when restricted to the class of grid graphs, i.e. graphs that, when drawn on an Euclidean Plane, form a specific regular tiling. A review of well--known results is given, and new results are presented. We aimed to find an algorithm that can find an exact solution for all the grid graphs, and, to do so, we present some important results: we prove a better lower-bound and present an upper-bound on the Roman Domination Number which improves the previous one and, we conjecture, is the Roman Domination Number for many, if not all, grid graphs.
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Woodring, Kimberly D. "Religion and Burial Roman Domination, Celtic Acceptance, or Mutual Understanding." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/etd/1158.

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The effects of Romanization were believed to be devastating to the cultures conquered by Rome, but Britain was an exception. The Romanization of Britain began through trade with the continent long before the invasion by Claudius. But the natives of Britain did not accept the Roman culture as completely as other conquests by Rome. R. G. Collingwood did not believe that the Romans dominated the Celtic culture. What he observed in the inscriptions and archaeology of Britain was a conflation of both cultures. Roman Britain was a unique combination of Celtic and Roman culture that was achieved through mutual acceptance and practice of both cultures’ values. The examination of two of those values, religious and mortuary practices, can help reveal the extent of Romanization in Britain and finally confirm Collingwood’s theory of Romanization.
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Russell, Haley D. "Italian Domination in Complementary Prisms." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3429.

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Let $G$ be any graph and let $\overline{G}$ be its complement. The complementary prism of $G$ is formed from the disjoint union of a graph $G$ and its complement $\overline{G}$ by adding the edges of a perfect matching between the corresponding vertices of $G$ and $\overline{G}$. An Italian dominating function on a graph $G$ is a function such that $f \, : \, V \to \{ 0,1,2 \}$ and for each vertex $v \in V$ for which $f(v)=0$, it holds that $\sum_{u \in N(v)} f(u) \geq 2$. The weight of an Italian dominating function is the value $f(V)=\sum_{u \in V(G)}f(u)$. The minimum weight of all such functions on $G$ is called the Italian domination number. In this thesis we will study Italian domination in complementary prisms. First we will present an error found in one of the references. Then we will define the small values of the Italian domination in complementary prisms, find the value of the Italian domination number in specific families of graphs complementary prisms, and conclude with future problems.
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Roux, Michel. "La colonisation militaire en Phrygie et son impact (IVe s. av. J.C.- IIIe s. après J.C.) : dynamiques spatiales, économiques et sociales." Thesis, Perpignan, 2018. http://www.theses.fr/2018PERP0023.

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L'objectif de cette thèse est d'étudier sur le long terme, depuis la fin de l'époque achéménide jusqu'à celle du Haut-Empire (aux alentours de 235 après J.-C.) l'implantation de troupes et de vétérans perses, gréco-macédoniens, thraces, lyciens et romains, puis de leurs descendants, dans l'espace phrygien, région quelque peu marginale située dans le centre-ouest de l'Anatolie. Après avoir dans la première partie identifié et justifié stratégiquement les différents lieux d'installation, elle examine l'impact économique de celle-ci au travers de l'étude de la mainmise sur la terre et ses productions, du rôle des soldats en tant que producteurs et consommateurs et de leur implication dans la sécurisation du territoire. Sur un plan social, le quotidien des militaires, des vétérans et de leurs familles est ensuite examiné, de même que les formes prises par leur domination sur le reste de la population et leurs choix religieux. Le tout s'appuie sur un vaste corpus de plusieurs centaines d'inscriptions et de monnaies
The objective of this thesis is to study on the long term, since the end of the achaemenid period until that of the roman Top-empire (near 235 AD) the setting-up of persian, greco-macedonian, thracian, lycian and roman troops and veterans, then of their descendants, in the Phrygian space, a little marginal region situated in west central Anatolia. Having in the first part identified and justified strategically the various places of installation, it examines the economic impact of this one through the study of the seizure by the earth and its productions, the role of the soldiers as producers and consumers and of their implication in the reassurance of the territory. On a social plan, the everyday life of the servicemen, the veterans and their families is then examined, as well as the forms taken by their domination on the rest of the population and their religious choices. The whole is based on a vast corpus of several hundred inscriptions and coins
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Haeussler, R. "The romanisation of Piedmont and Liguria." Thesis, University College London (University of London), 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268019.

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Nolassi, Salvatore Mario. "Algoritmi euristici per il Problema della Dominazione Romana." Doctoral thesis, Università di Catania, 2014. http://hdl.handle.net/10761/1560.

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Una funzione di Dominazione Romana su un grafo G è una funzione di copertura che assegna ai vertici del grafo uno tra i valori (0, 1, 2) con l'unico vincolo che ogni vertice con valore 0 abbia almeno un vicino con valore 2. Il peso di una funzione di Dominazione Romana è la somma di tutti i valori assegnati e il numero di Dominazione Romana di un grafo G è definito come il minimo tra tutte le funzioni di Dominazione Romana su G. Dopo un'introduzione ai concetti base che ruotano attorno alla Dominazione Romana, viene studiato il problema per due particolari classe di grafi, cioè grafi a griglia e i bipartiti. Per i grafi a griglia vengono prodotti degli schemi di copertura ottimali per griglie di qualsiasi dimensione e inoltre vengono migliorati i limiti superiori e inferiori noti del numero di Dominazione Romana. Per quanto riguarda i grafi bipartiti viene proposto un approccio che partendo da un insieme di vertex cover del grafo produce una funzione di Dominazione Romana in tempo polinomiale. Nel prosieguo della dissertazione vengono mostrati vari approcci euristici per qualsiasi classe di grafo. In particolare viene prodotto un algoritmo euristico che in tempo polinomiale calcola una copertura e un numero di Dominazione Romana che rientra nei limiti teorici noti introducendo un nuovo parametro associato ai vertici del grafo. Infine una delle varianti della stessa euristica è stata implementata su architettura CUDA permettendo la parallelizzazione del calcolo su GPU e saranno mostrate le strutture dati utilizzate e le problematiche riscontrate.
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Talon, Alexandre. "Intensive use of computing resources for dominations in grids and other combinatorial problems." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEN079.

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Nous cherchons à prouver de nouveaux résultats en théorie des graphes et combinatoire grâce à la vitesse de calcul des ordinateurs, couplée à des algorithmes astucieux. Nous traitons quatre problèmes. Le théorème des quatre couleurs affirme que toute carte d’un monde où les pays sont connexes peut être coloriée avec 4 couleurs sans que deux pays voisins aient la même couleur. Il a été le premier résultat prouvé en utilisant l'ordinateur, en 1989. Nous souhaitions automatiser encore plus cette preuve. Nous expliquons la preuve et fournissons un programme qui permet de la réétablir, ainsi que d'établir d'autres résultats avec la même méthode. Nous donnons des pistes potentielles pour automatiser la recherche de règles de déchargement.Nous étudions également les problèmes de domination dans les grilles. Le plus simple est celui de la domination. Il s'agit de mettre des pierres sur certaines cases d'une grille pour que chaque case ait une pierre, ou ait une voisine qui contienne une pierre. Ce problème a été résolu en 2011 en utilisant l’ordinateur pour prouver une formule donnant le nombre minimum de pierres selon la taille de la grille. Nous adaptons avec succès cette méthode pour la première fois pour des variantes de la domination. Nous résolvons partiellement deux autres problèmes et fournissons des bornes inférieures pour ces problèmes pour les grilles de taille arbitraire.Nous nous sommes aussi penchés sur le dénombrement d’ensembles dominants. Combien y a-t-il d’ensembles dominant une grille donnée ? Nous étudions ce problème de dénombrement pour la domination et trois variantes. Nous prouvons l'existence de taux de croissance asymptotiques pour chacun de ces problèmes. Pour chaque, nous donnons en plus un encadrement de son taux de croissance asymptotique.Nous étudions enfin les polyominos, et leurs façons de paver des rectangles. Il s'agit d'objets généralisant les formes de Tetris : un ensemble de carrés connexe (« en un seul morceau »). Nous avons attaqué un problème posé en 1989 : existe-t-il un polyomino d'ordre impair ? Il s'agit de trouver un polyomino qui peut paver un rectangle avec un nombre impair de copies, mais ne peut paver de rectangle plus petit. Nous n'avons pas résolu ce problème, mais avons créé un programme pour énumérer les polyominos et essayer de trouver leur ordre, en éliminant ceux ne pouvant pas paver de rectangle. Nous établissons aussi une classification, selon leur ordre, des polyominos de taille au plus 18
Our goal is to prove new results in graph theory and combinatorics thanks to the speed of computers, used with smart algorithms. We tackle four problems.The four-colour theorem states that any map of a world where all countries are made of one part can be coloured with 4 colours such that no two neighbouring countries have the same colour. It was the first result proved using computers, in 1989. We wished to automatise further this proof. We explain the proof and provide a program which proves it again. It also makes it possible to obtain other results with the same method. We give potential leads to automatise the search for discharging rules.We also study the problems of domination in grids. The simplest one is the one of domination. It consists in putting a stone on some cells of a grid such that every cell has a stone, or has a neighbour which contains a stone. This problem was solved in 2011 using computers, to prove a formula giving the minimum number of stones needed depending on the dimensions of the grid. We successfully adapt this method for the first time for variants of the domination problem. We solve partially two other problems and give for them lower bounds for grids of arbitrary size.We also tackled the counting problem for dominating sets. How many dominating sets are there for a given grid? We study this counting problem for the domination and three variants. We prove the existence of asymptotic growths rates for each of these problems. We also give bounds for each of these growth rates.Finally, we study polyominoes, and the way they can tile rectangles. They are objects which generalise the shapes from Tetris: a connected (of only one part) set of squares. We tried to solve a problem which was set in 1989: is there a polyomino of odd order? It consists in finding a polyomino which can tile a rectangle with an odd number of copies, but cannot tile any smaller rectangle. We did not manage to solve this problem, but we made a program to enumerate polyominoes and try to find their orders, discarding those which cannot tile rectangles. We also give statistics on the orders of polyominoes of size up to 18
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Books on the topic "Roman domination"

1

La domination: Roman. Paris: Grasset, 2008.

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Boucherville, Georges Boucher de. Nicolas Perrot, ou, Les coureurs des bois sous la domination française: Roman. Sainte-Foy, Québec: Éditions de la Huit, 1996.

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Native religion under Roman domination: Deities, springs and mountains in the north-west of the Iberian peninsula. Oxford: Archaeopress, 2005.

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L, James E. Cinquante nuances de grey: Roman. Paris: Editions Jean-Claude Lattès, 2012.

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Windsor, Rudolph R. Judea trembles under Rome: The untold details of the Greek and Roman military domination of Palestine during the time of Jesus of Galilee. Atlanta, Ga: Windsor Golden Series, 1994.

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Robert, Denis. La domination du monde. Paris: Julliard, 2006.

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Stancomb, William Michael. The history and coinage of the Greek cities on the coast of the Black Sea: From the time of the Greek colonisation to the period of Roman domination : with particular reference to the mint of Olbia. [s.l.]: typescript, 1994.

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Prête à succomber. Paris: Marabout, 2013.

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Jameson, Lauren. Prête à succomber, l'intégrale. Paris: Marabout, 2014.

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traducteur, Guillerme Rose, Bourbonnière Jocelyne traducteur, Degottex Cédric traducteur, Wright Suzanne, Wright Suzanne, Wright Suzanne, Wright Suzanne, Wright Suzanne, Wright Suzanne, and Wright Suzanne, eds. La meute du phénix. Paris: Milady, 2013.

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Book chapters on the topic "Roman domination"

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Chellali, Mustapha, Nader Jafari Rad, Seyed Mahmoud Sheikholeslami, and Lutz Volkmann. "Roman Domination in Graphs." In Topics in Domination in Graphs, 365–409. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-51117-3_11.

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Chellali, M., N. Jafari Rad, S. M. Sheikholeslami, and L. Volkmann. "Varieties of Roman Domination." In Developments in Mathematics, 273–307. Cham: Springer International Publishing, 2012. http://dx.doi.org/10.1007/978-3-030-58892-2_10.

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Fernau, Henning. "Roman Domination: A Parameterized Perspective." In SOFSEM 2006: Theory and Practice of Computer Science, 262–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11611257_24.

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Pagourtzis, Aris, Paolo Penna, Konrad Schlude, Kathleen Steinhöfel, David Scot Taylor, and Peter Widmayer. "Server Placements, Roman Domination and Other Dominating Set Variants." In Foundations of Information Technology in the Era of Network and Mobile Computing, 280–91. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-0-387-35608-2_24.

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Chapelle, Mathieu, Manfred Cochefert, Jean-François Couturier, Dieter Kratsch, Mathieu Liedloff, and Anthony Perez. "Exact Algorithms for Weak Roman Domination." In Lecture Notes in Computer Science, 81–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-45278-9_8.

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Zhao, Yancai, H. Abdollahzadeh Ahangar, Zuhua Liao, and M. Chellali. "(a, b)-Roman Domination on Cacti." In Advances in Intelligent Systems and Computing, 198–206. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-02777-3_18.

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Pushpam, P. Roushini Leely, and S. Padmapriea. "On Total Roman Domination in Graphs." In Theoretical Computer Science and Discrete Mathematics, 326–31. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64419-6_42.

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Liedloff, Mathieu, Ton Kloks, Jiping Liu, and Sheng-Lung Peng. "Roman Domination over Some Graph Classes." In Graph-Theoretic Concepts in Computer Science, 103–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11604686_10.

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Shang, Weiping, and Xiaodong Hu. "The Roman Domination Problem in Unit Disk Graphs." In Computational Science – ICCS 2007, 305–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-72588-6_51.

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Pushpam, P. Roushini Leely, and S. Padmapriea. "Erratum to: On Total Roman Domination in Graphs." In Theoretical Computer Science and Discrete Mathematics, E1. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64419-6_58.

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Conference papers on the topic "Roman domination"

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Gudgeri, Manjula C., Pallavi Sangolli, and J. Varsha. "Roman domination number of path related graphs." In THIRD VIRTUAL INTERNATIONAL CONFERENCE ON MATERIALS, MANUFACTURING AND NANOTECHNOLOGY. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0096475.

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Gudgeri, Manjula C., Varsha, and Pallavi Sangolli. "Extended Roman Domination of some graceful graphs." In THIRD VIRTUAL INTERNATIONAL CONFERENCE ON MATERIALS, MANUFACTURING AND NANOTECHNOLOGY. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0096414.

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Salah, Saba, Ahmed A. Omran, and M. N. Al-Harere. "Modern roman domination on two operations in certain graphs." In 3RD INTERNATIONAL SCIENTIFIC CONFERENCE OF ALKAFEEL UNIVERSITY (ISCKU 2021). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0067022.

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Reports on the topic "Roman domination"

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Incongruity between biological and chronologic age among the pupils of sports schools and the problem of group lessons effectiveness at the initial stage of training in Greco-Roman wrestling. Aleksandr S. Kuznetsov, March 2021. http://dx.doi.org/10.14526/2070-4798-2021-16-1-19-23.

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Abstract:
Considerable influence and compulsory dropout among those, who go in for GrecoRoman wrestling at the age of 10-13, does not take into account the level of individual biological development and integral demands domination claimed on too high general physical training (GPT) (4) normatives fulfillment. It corresponds with general situation in the system of education (6, 9). In spite of uneven speed of biological development (1, 8, 9), there are general demands claimed on physical training at school for age groups (5) in accordance with chronologic age. The same situation is at sports schools. Technical and physical training lessons at Greco-Roman wrestling school at the stage of initial training are organized according to general group principle. Research methods. Information sources analysis and summarizing, questionnaire survey, coaches’ experience summarizing, methods of mathematical statistics. Results. The received research results led to the following conclusion: it is possible to solve the problem of dropping out of Greco-Roman wrestling sports schools in terms of minimal loss in the quality of sports training by means of dividing the training groups into subgroups. There different normatives of material mastering and set by standard physical qualities development are used. For this purpose we created the training groups and subgroups of the set objectives realization at Greco-Roman wrestling sports schools.
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