Abstract: In a previous talk I discussed (among other results) the recent theorem of Ahuja and Tripathi which answers the following question: Given a finite set D of positive integers, for which integers n is there a graph of order n with degree set D? This time I will discuss (a) when there is a connected graph of order n with degree set D; and (b) when there is a tree of order n with degree set D. I will also discuss: Given an infinite set D of positive integers, when is there a countably infinite tree with degree set D?