TY - CHAP
T1 - Dominating Partitions
AU - Haynes, Teresa W.
AU - Hedetniemi, Stephen T.
AU - Henning, Michael A.
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2023.
PY - 2023
Y1 - 2023
N2 - n this chapter, we will focus largely on the property P that the set S is a dominating set. In the first sections of the chapter, we present results on the domatic number, that is, the maximum order of a partition of the vertex set of a graph into dominating sets. We also consider the same type of partitions for total domination and independent domination. In the final section of this chapter, we consider graphs whose vertex set can be partitioned into two specified types of dominating sets, for example a dominating set and a total dominating set.
AB - n this chapter, we will focus largely on the property P that the set S is a dominating set. In the first sections of the chapter, we present results on the domatic number, that is, the maximum order of a partition of the vertex set of a graph into dominating sets. We also consider the same type of partitions for total domination and independent domination. In the final section of this chapter, we consider graphs whose vertex set can be partitioned into two specified types of dominating sets, for example a dominating set and a total dominating set.
UR - http://www.scopus.com/inward/record.url?scp=85159121906&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-09496-5_12
DO - 10.1007/978-3-031-09496-5_12
M3 - Chapter
AN - SCOPUS:85159121906
T3 - Springer Monographs in Mathematics
SP - 353
EP - 379
BT - Springer Monographs in Mathematics
PB - Springer Science and Business Media Deutschland GmbH
ER -