Domination in graph theory


Walikar, On star-partition number of a graph. Hedetniemi, On the total domination of a graph. Under a Creative Commons license. Thus, Hence, we have proved that That is, the global domination number remains invariant under the operation of duplication of an edge in. If is a -set of then is a dominating set of. This implies that every -set of is a global dominating set of. For example, the global domination number of boolean function graph is discussed by Janakiraman et al.
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Dominator (graph theory)

Changing and Unchanging Domination. Vizing's conjecture relates the domination number of a cartesian product of graphs to the domination number of its factors. Figures a — c on the right show three examples of dominating sets for a graph. Furthermore, there is a simple algorithm that maps a dominating set to a set cover of the same size and vice versa. Walikar, On the graphs having unique minimum dominating sets, Abstract No. Domination in Graphs--Advanced Topics. Proceedings of Design and Test in Europe Conference:
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Fundamentals of Domination in Graphs - Teresa W. Haynes, Stephen Hedetniemi, Peter Slater - Google Книги

The independent domination number i G of a graph G is the size of the smallest independent dominating set or, equivalently, the size of the smallest maximal independent set. Graph Theory to appear. Retrieved 21 June The domination number of a graph , denoted , is the minimum size of a dominating set of vertices in , i. Dominating sets are of practical interest in several areas.
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Domination in graph theory
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On domination related concepts in Graph Theory

Domination in graph theory



Description: Dominating sets are of practical interest in several areas. Conversely, let D be a dominating set for G. Walikar, Some bounds on the connected domination number of a graph. Vizing's conjecture relates the domination number of a cartesian product of graphs to the domination number of its factors.

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