Graphic Sequence condition

Question

A sequence $d = (d_1,d_2,\dots , d_n)$ is graphic if there is a simple graph with degree sequence $d$

If $d = (d_1,d_2,d_3, \dots d_n)$ is graphic and $d_1 \geq d_2 \geq d_3 \geq \dots \geq d_n$ , then show that $\sum_{i=1}^{n}d_i$ is even and $$\sum_{i=1}^{k}d_i \leq \left [ k(k-1) + \sum_{i=k+1}^{n} \min\{k,d_i\} \right ] \quad ,1 \leq k \leq n$$.

Comments

can u tell what is graphic mean here?

Suppose I do with 3 points 3,2,1 then it is giving odd value.

---

A sequence $d = (d_1,d_2,\dots , d_n)$ is graphic if there is a simple graph with degree sequence $d$