Order, Size and Degree

Graphs have an order equal to the number of vertices that they contain.

The size of a graph is equal to the number of edges.

Complete graphs have the maximum size for a given order, without loops. For a graph of order n the maximum size will be \dfrac {n}{2}\left( n-1\right).

The degree of a vertex is equal to the number of edges that enter or leave it.

The maximum vertex degree for a given order, n, of graph without loops, is n-1.

The sum of vertex degrees will be double the size of the graph as each edge has two ends. Consequently a graph cannot have an odd number of vertices with an odd degree.