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Showing 1 to 5 of 5 for “"Total domination number"”.
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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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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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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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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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Matchings, Connectivity, and Eigenvalues in Regular Graphs
… we obtain the best lower bound for the matching number over $n$-vertex connected regular graphs in terms of edge-connectedness and determine when the matching number is minimized. We also establish the best upper bound for the number of cut-edges over $n$-vertex connected odd regular graphs and …