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 
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, 
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.