The term "null graph" is used both to refer to any empty graph and to the empty graph on 0 nodes.
Because of the conflicting usage, it is probably best to avoid use of the term altogether. This is especially the case when coupled with the fact that consideration of the 0-node empty graph as a graph in the first place is discouraged since it is felt by many in the graph theoretical community that allowing the null graph causes much more trouble than it is worth (Harary and Read 1973). For example, the null graph has no automorphism group, it cannot be imbedded on the sphere obeying the polyhedral formula, it is connected and acyclic but has too many edges to be a tree, and so on. According to Brendan McKay (2002), it is an exception to so many things that the community (or most of it) has decided that the only good null graph is a dead null graph.
