A survey of selected recent results on total domination in graphs
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This paper offers a survey of selected recent results on total domination in graphs and defines a set S of vertices in a graph G if every vertex of G is adjacent to some vertex in S.About:
This article is published in Discrete Mathematics.The article was published on 2009-01-01 and is currently open access. It has received 289 citations till now. The article focuses on the topics: Dominating set & Vertex (geometry).read more
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Total Domination in Graphs
Michael A. Henning,Anders Yeo +1 more
TL;DR: This paper obtains several results and bounds for the @a-total domination number of a graph G, a graph with no isolated vertex, which is the minimum cardinality of an @ a-total dominating set of G.
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Upper bounds on the k -forcing number of a graph
TL;DR: The results resolve a problem posed by Meyer about regular bipartite circulant graphs and present a relationship between the k -forcing number and the connected k -domination number.
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On matching and semitotal domination in graphs
TL;DR: This paper provides a characterization of minimal semitotal dominating sets in graphs and proves that if G is a connected graph on at least two vertices, then γ t 2 ( G) ?
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Transversals and domination in uniform hypergraphs
TL;DR: upper bounds on the domination number of a k-uniform hypergraph with minimum degree at least 1 are established, and it is proved that all the essential upper bounds can be written in the unified form @c(H)@?(an"H+bm"H)/(ak+b) for constants b>=0 and a>-b/k.
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Locating-total domination in claw-free cubic graphs
TL;DR: It is shown that the locating-total domination number of a claw-free cubic graph is at most one-half its order and the graphs achieving this bound are characterized.
References
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Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
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Fundamentals of domination in graphs
TL;DR: Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms are presented.
Book
Domination in graphs : advanced topics
TL;DR: A survey of domination-related parameters topics on directed graphs graphs can be found in this article with respect to the domination number bondage, insensitivity, and reinforcement of graph dominating functions.
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Easy problems for tree-decomposable graphs
TL;DR: Using a variation of the interpretability concept, it is shown that all graph properties definable in monadic second-order logic with quantification over vertex and edge sets can be decided in linear time for classes of graphs of fixed bounded treewidth given a tree-decomposition.