7. Let G be a loop-free undirected graph, where A = max,ev{deg(v)}. a) Prove that x(G) ≤ A+ 1. b) Find two types of graphs G, where x(G) = A +1.

7. Type the answer correctly.Do not use ChatGPT.

Let G be a loop-free undirected graph, where ∆ = max_v∈V {deg(v)}.
a) Prove that χ(G) ≤ ∆ + 1.
b) Find two types of graphs G, where χ(G) = ∆ + 1.