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Showing 1 to 8 of 8 for “"total domination"”.
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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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Total Domination Dot Critical and Dot Stable Graphs.
… is the 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 …
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Paired and Total Domination on the Queen's Graph.
<p>The Queen’s domination problem has a long and rich history. The problem can be simply stated as: What is the minimum number of queens that can be placed on a chessboard so that all squares are attacked or occupied by a queen? The problem has been expanded to include not only the standard 8x8 …
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Vertices in Total Dominating Sets.
… In this thesis the property of interest is total domination. The total domination number, <em>gamma<sub>t</sub></em>, is the cardinality of a smallest total dominating set in a graph. We investigate <em>gamma<sub>t</sub></em>-excellent, <em>gamma<sub>t</sub></em>-commendable, …
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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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Matchings, Connectivity, and Eigenvalues in Regular Graphs
… relationship between the matching number and the total domination number in regular graphs. In Chapter 3, we explore the relationship between eigenvalue and matching number in regular graphs. We give a condition on an appropriate eigenvalue that guarantees a lower bound for the matching number of …
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Topics in Probabilistic Combinatorics
… interested in a combinatorial game called the total domination game. Played on a graph $G$, the game involves two players, Dominator and Staller, alternately selecting vertices such that each chosen vertex increases the number of vertices totally dominated by the selected set. The game ends …
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Games, Graphs, and Groups
… for a cop-win in terms of the independence and domination numbers of $G$. In the *domination game*, two players called Dominator and Staller select vertices in a graph $G$ alternately. A vertex is said to be *dominated* if it has been selected or is adjacent to a selected vertex. Each selected …