Titlebook: Structures of Domination in Graphs; Teresa W. Haynes,Stephen T. Hedetniemi,Michael A. Book 2021 The Editor(s) (if applicable) and The Aut

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过滤

Domination and Total Domination in Hypergraphsvertex . in ., there exists an edge . ∈ .(.) for which . ∈ . and . ∩ (. ∖{.})≠∅. The domination number .(.) and the total domination number ..(.) are the minimum cardinalities of a dominating set and total dominating set, respectively, in .. This chapter presents an overview of research on domination and total domination in hypergraphs.

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Algorithms and Complexity of Power Domination in Graphsled a . if all vertices in .  are observed using rules (i) and (ii) when applied to .. The . ..(.) equals the minimum cardinality of a power dominating set in .. In this chapter we consider algorithms and complexity of computing the power domination number ..(.) in various classes of graphs ..

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ineffectual

1389-2177 students.First chapter includes a glossary of commonly used .This volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results.   The book is divided into 3 parts. The first part focuses on several domination-relat

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inquisitive

Fractional Domatic, Idomatic, and Total Domatic Numbers of a Graphimes any particular vertex appears in .. The fractional idiomatic and fractional total domatic numbers are defined analogously with all families . of independent dominating sets and total dominating sets of ., respectively. In this chapter, we survey some results on the three parameters and their re

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Dominator and Total Dominator Colorings in Graphsss, where a vertex dominates itself and all vertices adjacent to it. The dominator chromatic number of . is the minimum number of colors among all dominator coloring of .. A total dominator coloring of a graph . is a proper coloring of the vertices of . in which each vertex of the graph dominates ev

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erythema

The Private Neighbor Concepth is not in the closed neighborhood .[. −{.}] of any vertex in . −{.}. A property . of sets . of vertices is called . if every superset of a set . having property . also has property .. In this chapter, we show that a general concept of a vertex having a private neighbor emerges as the condition tha