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 -