Titlebook: Topics in Domination in Graphs; Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Book 2020 Springer Nature Switzerland AG 2020 Dominatio

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Signed and Minus Dominating Functions in Graphs,tion .. The . -domination number of a graph . is the minimum weight of a . -dominating function of .. When . = {0, 1}, {−1, 1}, or {−1, 0, 1}, we obtain the standard, signed, or minus domination numbers, respectively. In this chapter we survey the main results and open problems on signed and minus domination and their generalizations.

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Rainbow Domination in Graphs, weight of a .-rainbow dominating function of . is called the .-rainbow domination number, ..(.), of .. Equivalently, the .-rainbow domination number of a graph . is the domination number of the Cartesian product of . with the complete graph ... In this chapter, we survey main results on rainbow domination and related concepts in graphs.

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Global Domination, An important special case is when . is the complete graph with two factors, a subgraph . and its complement .. Representative results are presented, including those where the graphs are restricted to certain classes or the type of global domination is altered similar to what has occurred with standard domination.

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Restrained and Total Restrained Domination in Graphs,The restrained domination number of ., denoted by ..(.), is the smallest cardinality of a restrained dominating set of .. A total restrained dominating set is a set . such that every vertex . ∈ . is adjacent to a vertex in . and every vertex of . − . is adjacent to a vertex in . − .. The total restr

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