The Maximum and Minimum Degrees of a Graph

# The Maximum and Minimum Degrees of a Graph

Definition: For a graph $G = (V(G), E(G))$, the Maximum Degree of $G$ denoted by $\Delta (G)$, is the degree of the vertex with the greatest number of edges incident to it. The Minimum Degree of $G$ denoted by $\delta (G)$, is the degree of the vertex with the least number of edges incident to it. |

For example, consider the following graph:

The degree sequence of this graph is $(1, 2, 3, 3, 4, 4, 4, 4, 4)$. Hence $\Delta(G) = 4$, and $\delta (G) = 1$.