TY - CHAP

T1 - Broadcast Domination in Graphs

AU - Henning, Michael A.

AU - MacGillivray, Gary

AU - Yang, Feiran

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Dominating broadcast function

KW - Dominating set

UR - http://www.scopus.com/inward/record.url?scp=85105532842&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-58892-2_2

DO - 10.1007/978-3-030-58892-2_2

M3 - Chapter

AN - SCOPUS:85105532842

T3 - Developments in Mathematics

SP - 15

EP - 46

BT - Developments in Mathematics

PB - Springer

ER -