Titlebook: Domination in Graphs: Core Concepts; Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Book 2023 The Editor(s) (if applicable) and The Au

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Stephan von Cramon-Taubadel,Ludwig Striewe is the ability of a network to continue functioning in the presence of faults, such as a link failure (removing an edge) or a node failure (removing a vertex). In other cases, network performance can be enhanced by adding certain links (edges).

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Probabilistic Bounds and Domination in Random Graphs, 4, no tight bound on the domination number is yet known. When δ is sufficiently large, optimal bounds on the domination number can be found using the Probabilistic Method. We present several such probabilistic bounds, including one for the total domination number, in this chapter.

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Dominating Partitions,partitions for total domination and independent domination. In the final section of this chapter, we consider graphs whose vertex set can be partitioned into two specified types of dominating sets, for example a dominating set and a total dominating set.

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Domination Critical and Stable Graphs, is the ability of a network to continue functioning in the presence of faults, such as a link failure (removing an edge) or a node failure (removing a vertex). In other cases, network performance can be enhanced by adding certain links (edges).

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