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.
