Dominating functions in graphs

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6 Citations (Scopus)


For an arbitrary subset P of the reals, we define a function f. V → P to be a P-dominating function of a graph G = (V, E) if the sum of its function values over any closed neighbourhood is at least 1. That is, for every v ε V, f(N (v) U (v)) ≥ 1. The P-domination number of a graph G is defined to be the infimum of f(V) taken over all Pdominating functions f. When P = (0, 1) we obtain the standard domination number. When P = [0, 1], (-1, 0, 1) or (-1, 1) we obtain the fractional, minus or signed domination numbers, respectively. [n this chapter, we survey some recent results concerning dominating functions in which negative weights are allowed.

Original languageEnglish
Title of host publicationDomination in Graphs
Subtitle of host publicationAdvanced Topics
PublisherCRC Press
Number of pages30
ISBN (Electronic)0824700341, 9781351454643
ISBN (Print)9780824700348
Publication statusPublished - 1 Jan 2017
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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