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Dissertations / Theses on the topic 'Domination number'

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Published: 4 June 2021

Last updated: 26 July 2025

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1

Hopkins, Lora Shuler. "Bounds on total domination subdivision numbers." [Johnson City, Tenn. : East Tennessee State University], 2003. http://etd-submit.etsu.edu/etd/theses/available/etd-0223103-205608/unrestricted/HopkinsL031403f.pdf.

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2

Bukhary, Nisreen. "Domination in Benzenoids." VCU Scholars Compass, 2010. http://scholarscompass.vcu.edu/etd/2118.

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A benzenoid is a molecule that can be represented as a graph. This graph is a fragment of the hexagon lattice. A dominating set $D$ in a graph $G$ is a set of vertices such that each vertex of the graph is either in $D$ or adjacent to a vertex in $D$. The domination number $\gamma=\gamma(G)$ of a graph $G$ is the size of a minimum dominating set. We will find formulas and bounds for the domination number of various special benzenoids, namely, linear chains $L(h)$, triangulenes $T_k$, and parallelogram benzenoids $B_{p,q}$. The domination ratio of a graph $G$ is $\frac{\gamma(G)}{n(G)}$, wher

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3

Chukwukere, Presley. "The 2-Domination Number of a Caterpillar." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3456.

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A set D of vertices in a graph G is a 2-dominating set of G if every vertex in V − D has at least two neighbors in D. The 2-domination number of a graph G, denoted by γ2(G), is the minimum cardinality of a 2- dominating set of G. In this thesis, we discuss the 2-domination number of a special family of trees, called caterpillars. A caterpillar is a graph denoted by Pk(x1, x2, ..., xk), where xi is the number of leaves attached to the ith vertex of the path Pk. First, we present the 2-domination number of some classes of caterpillars. Second, we consider several types of complete caterpillars.

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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 dom

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Roux, Adriana. "On the (r,s)-domination number of a graph." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/86266.

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Thesis (PhD)--Stellenbosch University, 2014.<br>ENGLISH ABSTRACT: The (classical) domination number of a graph is the cardinality of a smallest subset of its vertex set with the property that each vertex of the graph is in the subset or adjacent to a vertex in the subset. Since its introduction to the literature during the early 1960s, this graph parameter has been researched extensively and nds application in the generic facility location problem where a smallest number of facilities must be located on the vertices of the graph, at most one facility per vertex, so that there is at least

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6

Jamieson, William. "General Bounds on the Downhill Domination Number in Graphs." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/honors/107.

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A path π = (v1, v2,...vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 < i < k, deg(vi) > deg(vi+1), where deg(vi) denotes the degree of vertex vi ∊ V. The downhill domination number equals the minimum cardinality of a set S ⊂ V having the property that every vertex v ∊ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order

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7

McCoy, Tabitha Lynn. "Cost Effective Domination in Graphs." Digital Commons @ East Tennessee State University, 2012. https://dc.etsu.edu/etd/1485.

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A set S of vertices in a graph G = (V,E) is a dominating set if every vertex in V \ S is adjacent to at least one vertex in S. A vertex v in a dominating set S is said to be it cost effective if it is adjacent to at least as many vertices in V \ S as it is in S. A dominating set S is cost effective if every vertex in S is cost effective. The minimum cardinality of a cost effective dominating set of G is the cost effective domination number of G. In addition to some preliminary results for general graphs, we give lower and upper bounds on the cost effective domination number of trees in terms o

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8

Rodriguez, Tony K. "Very Cost Effective Domination in Graphs." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etd/2345.

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A set S of vertices in a graph G=(V,E) is a dominating set if every vertex in V\S is adjacent to at least one vertex in S, and the minimum cardinality of a dominating set of G is the domination number of G. A vertex v in a dominating set S is said to be very cost effective if it is adjacent to more vertices in V\S than to vertices in S. A dominating set S is very cost effective if every vertex in S is very cost effective. The minimum cardinality of a very cost effective dominating set of G is the very cost effective domination number of G. We first give necessary conditions for a graph to have

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9

Cheney, Stephen R. "Domination Numbers of Semi-strong Products of Graphs." VCU Scholars Compass, 2015. http://scholarscompass.vcu.edu/etd/3989.

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This thesis examines the domination number of the semi-strong product of two graphs G and H where both G and H are simple and connected graphs. The product has an edge set that is the union of the edge set of the direct product of G and H together with the cardinality of V(H), copies of G. Unlike the other more common products (Cartesian, direct and strong), the semi-strong product is neither commutative nor associative. The semi-strong product is not supermultiplicative, so it does not satisfy a Vizing like conjecture. It is also not submultiplicative so it shares these two properties with th

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10

Kiser, Derek. "Distance-2 Domatic Numbers of Graphs." Digital Commons @ East Tennessee State University, 2015. https://dc.etsu.edu/etd/2505.

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The distance d(u, v) between two vertices u and v in a graph G equals the length of a shortest path from u to v. A set S of vertices is called a distance-2 dominating set if every vertex in V \S is within distance-2 of at least one vertex in S. The distance-2 domatic number is the maximum number of sets in a partition of the vertices of G into distance-2 dominating sets. We give bounds on the distance-2 domatic number of a graph and determine the distance-2 domatic number of selected classes of graphs.

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11

DesOrmeaux, Wyatt Jules. "Restrained and Other Domination Parameters in Complementary Prisms." Digital Commons @ East Tennessee State University, 2008. https://dc.etsu.edu/etd/1998.

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In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be pre

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12

Schmidt, Simon. "Jeux à objectif compétitif sur les graphes." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM085/document.

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Dans cette thèse nous étudions trois jeux à objectif compétitif sur les graphes. Les jeux à objectif compétitif proposent une approche dynamique des problèmes d'optimisation discrètes. L'idée générale consiste à associer à un problème d'optimisation (coloration, domination, etc.) un jeu combinatoire partisan de la façon suivante. Deux joueurs construisent tour à tour la structure reliée au problème d'optimisation. L'un d'eux cherche à ce que cette structure soit le plus optimale possible, tandis que l'autre essaye de l'en empêcher. Sous l'hypothèse que les deux joueurs jouent optimalement, la

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13

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'

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14

Gledel, Valentin. "Couverture de sommets sous contraintes." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSE1130.

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Cette thèse porte sur le problème de la couverture d'ensembles finis dans une structure discrète. Cette problématique très générale permet de nombreuses approches et nous faisons l'étude de certaines d'entre elles. Le premier chapitre introduit les notions qui seront indispensables à la bonne compréhension de cette thèse et fait un bref état de l'art sur certains problèmes de couvertures, en particulier le problème de domination dans les graphes. Le second chapitre aborde la domination de puissance, une variante du problème de domination qui a la particularité qu'on lui adjoint un phénomène de

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15

Janin, Floriane. "La comptabilité exposée : le cas du football français. : une comptabilité entre domination et émancipation." Thesis, Jouy-en Josas, HEC, 2015. http://www.theses.fr/2015EHEC0008.

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Cette thèse explore dans quelle mesure la comptabilité peut jouer un rôle dans le dévoilement et la remise en cause publics d’une situation de domination, et ainsi contribuer à une certaine forme d’émancipation. Au plus près des interprétations des acteurs, cette thèse suit les voix libérales dévoilant et remettant en cause la domination des discours et des principes de rationalisation et de régulation financières à l’œuvre dans le football professionnel français. La comptabilité du football français est particulièrement exposée, du fait de la médiatisation et de la financiarisation intenses d

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16

Jia, Wei. "Image analysis and representation for textile design classification." Thesis, University of Dundee, 2011. https://discovery.dundee.ac.uk/en/studentTheses/c667f279-d7a6-4670-b23e-c9dbe2784266.

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A good image representation is vital for image comparision and classification; it may affect the classification accuracy and efficiency. The purpose of this thesis was to explore novel and appropriate image representations. Another aim was to investigate these representations for image classification. Finally, novel features were examined for improving image classification accuracy. Images of interest to this thesis were textile design images. The motivation of analysing textile design images is to help designers browse images, fuel their creativity, and improve their design efficiency. In rec

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Guignard, Adrien. "Jeux de coloration de graphes." Thesis, Bordeaux 1, 2011. http://www.theses.fr/2011BOR14391/document.

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La thèse porte sur les deux thèmes des Jeux combinatoires et de la théorie des graphes. Elle est divisée en deux parties.1) Le jeu de Domination et ses variantes: Il s'agit d'un jeu combinatoire qui consiste à marquer les sommets d'un graphe de telle sorte qu'un sommet marqué n'ait aucun voisin marqué. Le joueur marquant le dernier sommet est déclaré gagnant. Le calcul des stratégies gagnantes étant NP-difficile pour un graphe quelconque, nous avons étudié des familles particulières de graphes comme les chemins, les scies ou les chenilles. Pour ces familles on peut savoir en temps polynomial s

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18

Simjour, Narges. "A New Optimality Measure for Distance Dominating Sets." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2941.

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We study the problem of finding the smallest power of an input graph that has <em>k</em> disjoint dominating sets, where the <em>i</em>th power of an input graph <em>G</em> is constructed by adding edges between pairs of vertices in <em>G</em> at distance <em>i</em> or less, and a subset of vertices in a graph <em>G</em> is a dominating set if and only if every vertex in <em>G</em> is adjacent to a vertex in this subset. The problem is a different view of the <em>d</em>-domatic number problem in which the goal is to find the maximum number of disjoint dominating sets in the <em>d</em>

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19

Nguyen, Van Kien [Verfasser], Winfried [Gutachter] Sickel, Aicke [Gutachter] Hinrichs, and Jan [Gutachter] Vybiral. "Function spaces of dominating mixed smoothness, Weyl and Bernstein numbers / Van Kien Nguyen ; Gutachter: Winfried Sickel, Aicke Hinrichs, Jan Vybiral." Jena : Friedrich-Schiller-Universität Jena, 2017. http://d-nb.info/117759840X/34.

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20

Xu, Zhi-Xiong, and 許智雄. "The study of Roman domination number." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/88729997653347165599.

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碩士<br>淡江大學<br>數學學系碩士班<br>102<br>Given a graph G = (V, E). We define a function f from V to {0, 1, 2}. The function f is called a Roman dominating function on G when satisfying the condition that every vertex v_i with f(v_i)=0 must be adjacent to at least one vertex v_j with f(v_j)=2. The weight of Roman dominating function f is the sum of the weight of each vertex of G. The minimum weight of all possible Roman dominating functions on G is the Roman domination number of G, denoted by γ_R (G). A spider graph G(k_1,k_2,k_3,…,k_t ) is the union of t paths〖 P〗_(k_1 ), 〖 P〗_(k_2 ), …, 〖 P〗_(k_t )wi

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Kuan, Yu-Ting, and 關玉婷. "A study of integer domination number." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/3kdwsb.

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碩士<br>國立交通大學<br>應用數學系所<br>105<br>Let G = (V,E) be a graph. For integer k ≥ 1, a function f : V →N∪{0} is a {k}-dominating function if for every v∈V,f(v)+Σ_uv∈E f(u)≥k. The weight of f is Σ_v∈V f(v). The {k}-domination number, denoted by γ_{k}(G), of G is the minimum weight of a {k}-dominating function. Clearly, when k = 1, a {k}-domination problem is exactly the domination problem. Therefore, this study is a generalization of the domination problem on graphs. In this thesis, we obtain a good estimation of γ_{k}(G) for all graphs. And we focus on grid graphs P_m□P_n. As a consequence, we determ

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Chen, Wen-Wei, and 陳文暐. "Connected Domination Number in Circulant Graphs." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/f4vm83.

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碩士<br>國立交通大學<br>應用數學系所<br>105<br>Let G be a graph. A set S⊆V(G) is a connected dominating set of G if S is a dominating set of G and the subgraph induced by S is connected. The minimum size among connected dominating sets of G is the connected domination number of G, denoted by γ_c(G). For an integer n, let D be a subset of {1,2,...,⌊n/2⌋}. A circulant graph of order n with the jump set D, denoted by G(n;D), is a graph whose vertex set and edge set are, respectively, defined by V(G(n;D)) = {v_i | i ∈ {0,1,...,n-1}}, and E(G(n;D)) = {{v_i,v_j} | |i-j|_n ∈ D, i,j ∈ {0,1,...,n-1}}, where |i-j|_n

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Vo, Thi Nhu Mai. "On the domination number of grid graphs." Thesis, 1988. http://spectrum.library.concordia.ca/3816/1/ML49113.pdf.

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Jhen, Shou-Bo, and 鄭守博. "Weighted Distance Two Domination Number Of Graphs." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/20865936501878309973.

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碩士<br>國立嘉義大學<br>資訊工程學系研究所<br>99<br>Motivated by the resource sharing problem, this thesis deals with a variation of the domination problem which is referred to distance-two domination problem. Given a vertex subset D of graph G, which indicates the resource allocation, the vertices in D have full authority to access the resource, hence each of them has the weight three. For those vertices that are adjacent to a vertex (say v) in D may access the resource through v, they get weight two which is less than the weight of the vertices in set D. The vertices which are at distance two from the reso

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Wang, Wen, and 王文. "Domination number of Cartesian product of graphs." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/45008939229221822272.

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碩士<br>國立中山大學<br>應用數學系研究所<br>101<br>For a graph G, (G) is the domination number of G. Vizing [2] conjectured that gamma(G Box H) >= gamma(G)gamma(H) for any graph G and H, where G Box H is the Cartesian product of graphs G and H. Clark and Suen [1] proved that gamma(G Box H) >= gamma(G)gamma(H) for any graphs G and H. Barcalkin and German [5] proved that Vizing''s conjecture holds for some speci c family of graphs. We combine both of their approaches and prove that if G has k disjoint complete subgraphs G1;G2; : : :Gk and gamma_G(UG_i i = 1 to k ) = k, then gamma(G Box H) >= k gam

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Lin, Xuan-Yun, and 林軒筠. "Integer {k}-Domination Number of Circulant Graphs." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/6ntxrs.

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碩士<br>國立交通大學<br>應用數學系所<br>106<br>Let G(V,E) be a simple graph, i.e., G is undirected, no multiple edges and loopless. Let k be a positive integer. A function f: V(G)→Ν∪{0} is an integer {k}-dominating function if ∀v∈V(G), f(v)+∑_(uv∈E(G))▒〖f(u)≥〗 k. In addition, for all integer {k}-dominating functions f of G, 〖min┬f ∑_(x∈V(G))▒〖f(x)〗〗⁡ is the integer {k}-domination number of G (denoted byγ_({k})(G)). The problem of integer {k}-dominating number is necessary since the starting value k=1 is exactly the problem of domination number. Therefore, it is important to consider a version which general

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Chen, Min-Ling, and 陳旻琳. "A Study of Signed Domination Number of Torus Graphs." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/50507851958094276674.

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碩士<br>國立東華大學<br>資訊工程學系<br>101<br>Let G = (V;E) be a simple graph. A signed dominating function assigns 1 and -1 to each vertex such that the sum of the assigned values of the closed neighborhood of vertex v for each vertices for graph is more than 0. The signed domination number is the minimum sum among all possible signed dominating functions. In this thesis, we give some lower and upper bounds of the signed domination number for a torus graph. In particular, for some cases, our upper bounds are optimal.

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Liu, Ting-Wei, and 劉庭崴. "Upper Bounds on k-rainbow Domination Number of Sierpiński Graphs." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/edz49c.

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碩士<br>明志科技大學<br>工業工程與管理系碩士班<br>102<br>The k-rainbow domination is a variant of the classical domination problem in graphs and is defined as follows. Given an undirected graph G = (V, E), we have a set C with k colors and assign an arbitrary subset of these colors to each vertex of G. If a vertex is assigned an empty set, then the union of color sets of its neighbors must be C. This assignment is called the k-rainbow dominating function of G. The minimum sum of numbers of assigned colors over all vertices of G is called the k-rainbow domination number of G. In this paper, we give some algorithm

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Chiu, Yu-Chieh, and 邱鈺傑. "Self-stabilizing minimal dominating set algorithms of distributed systems and the signed star domination number of Cayley graphs." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/28741059665723204862.

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博士<br>國立交通大學<br>應用數學系所<br>102<br>The study of the domination problem in graph theory began in the nineteen-sixties. A distributed system such as an ad hoc network can be modeled by an undirected simple graph G = (V;E), where V represents the set of nodes (i.e., processes) and E represents the set of interconnections between processes of the distributed system. A subset D of the vertex set V of G is a dominating set if each vertex v in V is either a member of D or adjacent to a vertex in D. A dominating set of G is a minimal dominating set (MDS) if none of its proper subsets is a dominating set

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Chybová, Lucie. "Šachové úlohy v kombinatorice." Master's thesis, 2017. http://www.nusl.cz/ntk/nusl-367590.

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This master thesis discusses various mathematical problems related to the placement of chess pieces. Solutions to the problems are mostly elementary (yet sometimes quite inventive), in some cases rely on basic knowledge of graph theory. We successively focus on different chess pieces and their tours on rectangular boards, and then examine the "independence" and "domination" of chess pieces on square boards. The text is complemented with numerous pictures illustrating particular solutions to given problems.

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"Bounds on Total Domination Subdivision Numbers." East Tennessee State University, 2003. http://etd-submit.etsu.edu/etd/theses/available/etd-0223103-205608/.

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Yu, Li-Cheng, and 余立晟. "On domination numbers of directed tori." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/87837262742356634342.

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碩士<br>國立臺北商業技術學院<br>資訊與決策科學研究所<br>99<br>A dominating set in a graph G is a set S of vertices having the property that every vertex is either in S or dominated by S. The domination number (G) of G is the cardinality of a smallest dominating set in G. The dominating set problem concerns testing whether (G) 6 K for a given graph G and input K; it is a classical NP-complete decision problem in computational complexity theory. Therefore it is believed that there is no efficient algorithm that finds a smallest dominating set for a given graph. Let C_n denote the directed cycle of length n. For m, n>

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Lunney, Scott. "Trees with equal broadcast and domination numbers." Thesis, 2011. http://hdl.handle.net/1828/3746.

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A broadcast on a graph G=(V,E) is a function f : V → {0, ..., diam(G)} that assigns an integer value to each vertex such that, for each v ∈ V , f (v) ≤ e(v), the eccentricity of v. The broadcast number of a graph is the minimum value of Σv∈V f (v) among all broadcasts f with the property that for each vertex x of V, f (v) ≥ d(x, v) for some vertex v having positive f (v). This number is bounded above by both the radius of the graph and its domination number. Graphs for which the broadcast number is equal to the domination number are called 1-cap graphs. We investigate and characterize a cla

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Lin, Ming-Hung, and 林銘宏. "On the domination numbers of prisms of cycles." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/2em69h.

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碩士<br>國立中山大學<br>應用數學系研究所<br>96<br>Let $gamma(G)$ be the domination number of a graph $G$. For any permutation $pi$ of the vertex set of a graph $G$, the prism of $G$ with respect to $pi$ is the graph $pi G$ obtained from two copies $G_{1}$ and $G_{2}$ of $G$ by joining $uin V(G_{1})$ and $vin V(G_{2})$ iff $v=pi(u)$. We prove that $$gamma(pi C_{n})geq cases{frac{ n}{ 2}, &if $n = 4k ,$ cr leftlceilfrac{n+1}{2} ight ceil, &if $n eq 4k$,} mbox{and } gamma(pi C_{n}) leq leftlceil frac{2n-1}{3} ight ceil mbox{for all }pi.$$ We also find a permutation $pi_{t}$ such that $gamma(pi_{t} C_{n})=k$, whe

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Tu, Kuo-Hao, and 杜國豪. "Outer-connected domination numbers of trees and block graphs." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/tq82nu.

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碩士<br>國立東華大學<br>應用數學系<br>100<br>Given a graph G, a set S is an outer-connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by V∖S is connected. The outer-connected domination number r_c(G) is the minimum size of such a set. In this thesis, we present a linear-time algorithm for the outer-connected domination problem in trees and block graphs, and gives formulas to compute the outer-connected domination numbers of full k-ary trees.

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Hwang, Jenn Jia, and 黃振家. "The Domination and Bondage Numbers of Paths and Cycles." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/24600537879790177072.

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Abstract:

碩士<br>國立臺灣科技大學<br>資訊管理系<br>90<br>Let u and v be two vertices in a simple graph G=(V,E), where V and E are the vertex and edge, respectively, sets of G. We say that u k-dominates v if their distance is less than or equal to k. A subset D of V is called a k-dominating set of G if for every vertex v in V there exists some vertex u in D which k-dominates v. If the cardinality of D is minimum among all k-dominating sets, then is said to be the minimum k-domination number, denoted γk(G), of G. The k-bondage number of G, bk(G), is the number of edges whose removed results in γk(G-S)＞γk(G), where S

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37

王奕倫. "Signed star domination and signed star domatic numbers of complete bipartite graphs and an improved algorithm for network planarization." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/02364217719187379697.

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