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: Is the empty graph connected?My question is, which one is the more accepted definition?
Is a tree with $0$ vertices, $0$ edges or $1$ vertex, $0$ edges considered a valid tree?
graph theory;terminology;graphs;trees