TY - CHAP
T1 - Domination and Vizing’s Conjecture
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 - In this chapter, we study Vizing’s Conjecture from 1968 which asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. The conjecture was first posed by Vizing as a question in 1963. Vizing’s Conjecture is considered by many to be the main open problem in the area of domination in graphs. We also present Vizing-like conjectures for the total domination number, the independent domination number, the independence number, the upper domination number, and the upper total domination number in Cartesian products of graphs.
AB - In this chapter, we study Vizing’s Conjecture from 1968 which asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. The conjecture was first posed by Vizing as a question in 1963. Vizing’s Conjecture is considered by many to be the main open problem in the area of domination in graphs. We also present Vizing-like conjectures for the total domination number, the independent domination number, the independence number, the upper domination number, and the upper total domination number in Cartesian products of graphs.
UR - http://www.scopus.com/inward/record.url?scp=85159052549&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-09496-5_18
DO - 10.1007/978-3-031-09496-5_18
M3 - Chapter
AN - SCOPUS:85159052549
T3 - Springer Monographs in Mathematics
SP - 525
EP - 548
BT - Springer Monographs in Mathematics
PB - Springer Science and Business Media Deutschland GmbH
ER -