Results 221 to 230 of about 41,065 (264)

Total Dominating Sets in Maximal Outerplanar Graphs [PDF]

open access: possibleGraphs and Combinatorics, 2017
A set \(D\subseteq V(G)\) is a total domination set of graph \(G\) if every vertex from \(V(G)\) has a neighbor in \(D\). The minimum cardinality of a total domination set of \(G\) is called total domination number and is denoted by \(\gamma_t(G)\). A recent result from \textit{M. Dorfling} et al. [Discrete Math. 339, No.
Lemańska, Magdalena   +2 more
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INTERIOR TOTAL DOMINATING SETS IN GRAPHS

Advances and Applications in Discrete Mathematics, 2018
Summary: Let \(G = (V(G)\), \(E(G))\) be a simple graph. A total dominating set \(D\) of \(V(G)\) is an interior total dominating set of \(G\) if every \(v\in D\) is an interior vertex of \(G\). The minimum cardinality of an interior total dominating set of \(G\), denoted by \(\gamma_{lt}(G)\) is called an interior total domination number of \(G\).
Pacardo, Shiela Mae B., Rara, Helen M.
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Graphs with few total dominating sets

Discrete Mathematics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marcin Krzywkowski, Stephan Wagner
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Total Dominating Set Games

2005
In this paper, we consider cooperative games arising from total domination problem on graphs. We introduce two games, rigid total dominating set game and relaxed total dominating set game, and focus on their cores. First, a common necessary and sufficient condition for the balancedness of the two total dominating set games is obtained.
Qizhi Fang, Hye Kyung Kim, Dae Sik Lee
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A Characterization of Graphs with Disjoint Dominating and Total Dominating Sets

Quaestiones Mathematicae, 2009
A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. In this paper, we provide a constructive characterization of graphs whose vertex set can be partitioned into a ...
Henning, Michael A, Southey, Justin
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Connected Total Dominating Sets and Connected Total Domination Polynomials of Square of Paths

International Journal of Mathematics Trends and Technology, 2014
Let G be a simple connected graph of order n. Let Dct(G, i) be the family of connected total dominating sets in G with cardinality i. The polynomial Dct (G, x) = n i (G) ct    dct (G, i) x is called the connected total domination polynomial of G. In this paper, we obtain a recursive formula for dct ( 2 n P , i).
A Vijayan, T. Anitha Baby
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