Q45

Let $G$ be a simple, finite, undirected graph with vertex set $\left\{v_{1}, \ldots, v_{n}\right\}$. Let $\Delta(G)$ denote the maximum degree of $G$ and let $\mathbb{N}=\{1,2, \ldots\}$ denote the set of all possible colors. Color the vertices of $G$ using the following greedy strategy: for $i=1, \ldots, n$ $\operatorname{color}\left(v_{i}\right) \leftarrow \min \left\{j \in \mathbb{N}\right.$ : no neighbour of $v_{i}$ is colored $\left.j\right\}$ Which of the following statements is/are $\text{TRUE}?$