@inbook{9a5cae04edce483a9109745fbc1c829d,

title = "Fractional Domatic, Idomatic, and Total Domatic Numbers of a Graph",

abstract = "The fractional domatic number of a graph G is the maximum ratio | ℱ| ∕ m(ℱ) over all families ℱ of dominating sets of G, where m(ℱ) denotes the maximum number of times any particular vertex appears in ℱ. The fractional idiomatic and fractional total domatic numbers are defined analogously with all families ℱ of independent dominating sets and total dominating sets of G, respectively. In this chapter, we survey some results on the three parameters and their relationship with and extension to hypergraphs.",

keywords = "Fractional domatic number, Fractional idomatic number, Fractional total domatic number, Hypergraph",

author = "Wayne Goddard and Henning, {Michael A.}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-58892-2_4",

language = "English",

series = "Developments in Mathematics",

publisher = "Springer",

pages = "79--99",

booktitle = "Developments in Mathematics",

address = "Germany",

}