  Recently, Haynes, Hedetniemi and Henning published the book Topics in
Domination in Graphs, which comprises 16 contributions that present advanced
topics in graph domination, featuring open problems, modern techniques, and
recent results. One of these contributions is the chapter Multiple Domination,
by Hansberg and Volkmann, where they put into context all relevant research
results on multiple domination that have been found up to 2020. In this note,
we show how to improve some results on double domination that are included in
the book.
