[Math] Proof related to minimum and maximum degree of vertices of an undirected graph

graph theory

I don't know how to proceed for this problem. I would appreciate any help. Thanks!

Let $\delta$ and $\Delta$ be the minimum and maximum degree of the
vertices of an undirected graph G.

Show that $\delta \leq \frac{2\left | E(G) \right |}{\left | V(G)
\right |}\leq \Delta $.

Best Answer

HINT: Use the basic fact relating degrees of vertices to number of edges: $$\sum_{v\in V(G)}\deg v=2|E(G)|\;.$$ What are the minimum and maximum possible values of the sum?

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