The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are TRUE?

Let us analyze each statement for the Petersen graph $G = (V, E)$ with $|V| = 10$ and $|E| = 15$:

• (A) True: The Petersen graph contains odd cycles (it has 5-cycles, and its girth is 5), so it is not bipartite and requires at least 3 colors. It can be 3-colored (for instance, color the outer 5-cycle with colors $1, 2, 1, 2, 3$ and color the corresponding adjacent inner vertices properly with $3, 3, 2, 1, 1$). Hence, its chromatic number is $\chi(G) = 3$.

• (B) True: The Petersen graph is famous for being non-Hamiltonian (it does not contain a Hamiltonian cycle), but it does possess a Hamiltonian path (a simple path visiting all 10 vertices).

• (C) True: The graph shown is a known 3-regular graph with 10 vertices, girth 5, and diameter 2. It is isomorphic to the Petersen graph.

• (D) False: The independence number (size of the maximum independent set) of the Petersen graph is $\alpha(G) = 4$, not 3 (e.g., choosing two independent vertices from the outer 5-cycle and two independent vertices from the inner star).