An empty graph on 
nodes consists of 
isolated nodes with no
edges. Such graphs are also
commonly called edgeless graphs (Zafarani et al. 2014, p. 37; Kitaev
et al. 2021) and sometimes null graphs (though the term "null
graph" is also used to refer in particular to the empty graph on 0 nodes).
An empty graph is therefore not a nonempty graph,
regardless of how many vertices it has.
The empty graph on 0 nodes is (sometimes) called the null graph and the empty graph on 1 node
is called the singleton graph. The empty graph
on 
vertices
is the graph complement of the complete
graph 
,
and is commonly denoted 
.
The notation 
is apparently also used by some authors (e.g., Tyshkevich 2000, Fact 2), but not
recommended as it conflicts with use of this notation for an odd
graph among others.
The empty graph on 
nodes can be generated in the Wolfram
Language as Graph[Range[n],
] or FromEntity[Entity["Graph",
"Empty", n]
], and precomputed properties of empty
graphs are available in the Wolfram Language
using GraphData[
"Empty", n
].
The bipartite double graph of the empty graph 
is 
.
Empty graphs are (trivially) dominating unique.
A graph can be tested for being empty in the Wolfram Language using EmptyGraphQ.
