TY - CHAP

T1 - Restrained and Total Restrained Domination in Graphs

AU - Hattingh, Johannes H.

AU - Joubert, Ernst J.

N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020

Y1 - 2020

N2 - Let G = (V, E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted by γr(G), is the smallest cardinality of a restrained dominating set of G. A total restrained dominating set is a set S such that every vertex v ∈ V is adjacent to a vertex in S and every vertex of V − S is adjacent to a vertex in V − S. The total restrained domination number of G, denoted by γtr(G), is the smallest cardinality of a total restrained dominating set of G. In this chapter, we survey results on restrained and total restrained domination in graphs.

AB - Let G = (V, E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted by γr(G), is the smallest cardinality of a restrained dominating set of G. A total restrained dominating set is a set S such that every vertex v ∈ V is adjacent to a vertex in S and every vertex of V − S is adjacent to a vertex in V − S. The total restrained domination number of G, denoted by γtr(G), is the smallest cardinality of a total restrained dominating set of G. In this chapter, we survey results on restrained and total restrained domination in graphs.

UR - http://www.scopus.com/inward/record.url?scp=85093858612&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-51117-3_5

DO - 10.1007/978-3-030-51117-3_5

M3 - Chapter

AN - SCOPUS:85093858612

T3 - Developments in Mathematics

SP - 129

EP - 150

BT - Developments in Mathematics

PB - Springer

ER -