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Showing 1 to 20 of 23 for “"Domination number"”.
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Total Domination Dot Critical and Dot Stable Graphs.
… union of their neighborhoods. A graph is total domination dot-critical if identifying any pair of adjacent vertices decreases the total domination number. On the other hand, a graph is total domination dot-stable if identifying any pair of adjacent vertices leaves the total domination number …
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Restrained and Other Domination Parameters in Complementary Prisms.
<p>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 …
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On Topological Indices And Domination Numbers Of Graphs
… stability of chemical compounds. The concepts of domination number and independent domination number, introduced from the mid-1860s, are very fundamental in Graph Theory. In this dissertation, we provide new theoretical results on these two topics. We study k-trees and cactus graphs with the sharp …
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Cost Effective Domination in Graphs
… set of <em>G</em> 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 of their domination number and characterize the trees that achieve the upper …
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Paired-Domination in Grid Graphs.
… the subgraph induced by <em>S</em>. The domination number of a graph <em>G</em> is the smallest cardinality of any dominating set of <em>G</em>, and the paired-domination number is the smallest cardinality of any paired-dominating set. Determining the domination number for grid graphs is …
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Power Domination in graphs
Domination in graphs has been studied since the 1800s. Many parameters related to domination have been defined and studied since then. Power domi-nation was first defined and studied in the early 2000s. It is an abstraction of how an electrical power system is monitored. In this thesis, we focus on …
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Topics In Probabilistic Combinatorics
… the paper. Chapter 2 introduces the independent domination number. It is then shown that in the random graph model G(n,p) with probability tending to one, the independent domination number is one of two values. Also, the the number of independent dominating sets of given cardinality is analyzed …
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Domination in Sparse Graphs
… set that is the union of parts of pi. The pi-domination number gamma(G,pi) of G is the size of a smallest pi-dominating set. If each Vi in pi has size at most 2, we call pi a coupling of G and say that the vertices in Vi are coupled together. The coupled domination number, gamma cpl(G), is the …
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Independent Domination Of Subcubic Graphs
Let G be a simple graph. The independent domination number i(G) is the minimum cardinality among all maximal independent sets of G. A graph is subcubic whenever the maximum degree is at most three. In this paper, we will show that the independent domination number of a connected subcubic graph of …
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Global Domination Stable Graphs
… global dominating set of <i>G</i> is the global domination number of <i>G</i>. We explore the effects of graph modifications on the global domination number. In particular, we explore edge removal, edge addition, and vertex removal.</p>
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Bounds on Total Domination Subdivision Numbers.
<p>The domination subdivision number of a graph is the minimum number of edges that must be subdivided in order to increase the domination number of the graph. Likewise, the total domination subdivision number is the minimum number of edges that must be subdivided in order to increase the total …
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Placing Monitoring Devices in Electric Power Networks Modeled by Block Graphs.
… a power dominating set of a graph is its power domination number. In this thesis, we investigate the power domination number of a block graph.</p>
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Locating-Domination in Complementary Prisms.
… where <em>v</em> ≠ <em>u</em>. The locating-domination number of <em>G</em> is the minimum cardinality of a locating-dominating set of <em>G</em>. In this thesis, we study the locating-domination number of complementary prisms. We determine the locating-domination number of <em>GG̅</em> for …
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Domination in graphs: Vizing's conjecture
… remains one of the biggest open problems in domination in graph theory today. The conjecture states that the domination number of the Cartesian product of two graphs is at least as large as the product of the domination numbers of the two factor graphs. The aim of this thesis is to study the …
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Double Domination of Complementary Prisms.
… every vertex of <em>G</em> twice. The <em>double domination number</em>, denoted γ<sub>×2</sub>(<em>G</em>), is the cardinality of a minimum double dominating set of <em>G</em>. We have proven results on graphs of small order, specific families and lower bounds on γ<sub>×2</sub>(GG̅).</p>
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Liar's Domination in Grid Graphs
<p>As introduced by Slater in 2008, liar's domination provides a way of modeling protection devices where one may be faulty. Assume each vertex of a graph <em>G</em> is the possible location for an intruder such as a thief. A protection device at a vertex <em>v</em> is assumed to be able to detect …
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Extremal problems in graph theory
… twisted hypercubes of small radius and find the domination number of the Kneser graph $K(n,k)$ when $n\ge{3\over4}k\sp2\pm k,$ depending on whether k is even or odd. The path chromatic number $\chi\sb{P}(G)$ of a graph G is the least number of colors with which the vertices of G can be colored so …
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Explorations in the Classification of Vertices as Good or Bad.
… triple of nonnegative integers representing the domination number of <em>γ</em>(<em>G</em>), <em>g</em>(<em>G</em>), and <em>b</em>(<em>G</em>), respectively, and provide constructions of graphs meeting those conditions. We define the goodness index of a vertex <em>v</em> in a graph <em>G</em> as …
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Vertices in Total Dominating Sets.
… in a <em>rho-set</em>. Let <em>g</em> denote the number of <em>rho-good</em> vertices and <em>b</em> denote the number of <em>rho-bad</em> vertices. A graph <em>G</em> is called <em>rho-excellent</em> if every vertex in <em>V</em> is <em>rho</em>-good, <em>rho-commendable</em> if <em>g</em> > …
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Colourings, dominating sets and wreaths
… sets. We show that all forests with a given domination number $\gamma$ have at most ${5}^{\gamma/2}$ minimum dominating sets. Furthermore, for each $\gamma$, we construct a tree with domination number $\gamma$ which has more than $\frac{2}{5}{5}^{\gamma/2}$ minimum dominating sets. We also …
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