For the following $2$ cases:
(1) $V = \emptyset, E = \emptyset $ (i.e. nothing at all)
(2) $V = \{v_0\}, E = \emptyset $ (i.e. only 1 root node $v_0$)
Are they considered a valid tree? It seems like different literature have different definitions.
I recall that I have read a data structures and algorithms book that defines "A tree is a set of nodes that either: is empty or has a designated node, called the root ...". According to this definition, (1) and (2) are both valid trees. I don't have the book on hand, but I am sure if you search the quoted sentence above in Google, you can get lots of results, as quite a lot of lecture notes follow this definition.
However, another definition of trees often met is defined in terms of graphs:
A tree is "a connected graph without a cycle".
Using this definition, my question is transformed to another question: "Is an empty graph a connected graph?" But the answer to the latter question is debatable according to here:
My question is, which one is the more accepted definition?