Broadcast Domination in Graphs

Michael A. Henning, Gary MacGillivray, Feiran Yang

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

7 Citations (Scopus)

Abstract

For a graph G, a function f : V (G) →{0, 1, …, diam(G)} is a broadcast on G, where diam(G) denotes the diameter of G. For each vertex v in G, the value f(v) is the strength of the broadcast from v. For each vertex u ∈ V (G), if there exists a vertex v in G (possibly, u = v) such that f(v) > 0 and d(u, v) ≤ f(v), where d(u, v) is the distance betweenu and v, then f is called a dominating broadcast on G. The cost of the dominating broadcast f is the sum of the strengths of the broadcasts over all vertices in G, that is, the quantity ∑v ∈ Vf(v). The minimum cost of a dominating broadcast is the broadcast domination number of G. In this chapter, we survey selected results on the broadcast domination number of a graph.

Original languageEnglish
Title of host publicationDevelopments in Mathematics
PublisherSpringer
Pages15-46
Number of pages32
DOIs
Publication statusPublished - 2021

Publication series

NameDevelopments in Mathematics
Volume66
ISSN (Print)1389-2177
ISSN (Electronic)2197-795X

Keywords

  • Dominating broadcast function
  • Dominating set

ASJC Scopus subject areas

  • General Mathematics

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