Unless stated otherwise, graph means finite, simple and undirected; orders, sizes and empty-set conventions are fixed here

For a graph $G=(V,E)$ (A finite simple graph is a finite vertex set together with a set of two-element vertex subsets), its order is $|V|$ and its size is $|E|$ (The cardinality $\lvert A\rvert$ of a finite set). The null graph has $V=\varnothing$ and $E=\varnothing$. An edgeless graph has $E=\varnothing$ but may have vertices. Thus the null graph is the unique graph with no vertices, while an edgeless graph need not be null.

All sums indexed by $V$ or $E$ use their ordinary empty values. A minimum or maximum taken over the vertex set is used only when $V\ne\varnothing$; in particular, minimum and maximum degree are not assigned values for the null graph. Connectivity conventions for the null graph and the one-vertex graph are stated with the definition of connectivity.