ABSTRACT
Recall the definitions of graphs from Section 1.1.4. The degree of the vertex x was defined to be the number of edges that have x as an endpoint. We write degG (x) for the degree of x in graph G, or simply deg(x) if only one graph is being discussed. A graph is regular if all vertices have the same degree, and in particular a regular graph of degree 3 is called cubic. We denote the smallest of all degrees of vertices of G by δ(G), and the largest by Δ(G).
