What is the Degree of a Vertex? | Graph Theory Basics

A vertex cover of a graph G=(V, E) is a subset of vertices S ⊆V that includes at least one endpoint of every edge in E . Give a linear-time algorithm for the following task. Input: An undirected tree T=(V, E) Output: The size of the smallest vertex cover of T. For instance, in the following tree, possible vertex covers include {A, B, C, D, E, F, G} and {A, C, D, F} but not {C, E, F} . The smallest vertex cover has size 3:{B, E, G} | Numerade

From the proof of Theorem 34.12, we know that the vertex-cover problem and the NP-complete clique problem are complementary in the sense that an optimal vertex cover is the complement of a maximum-size clique in the complement graph. Does this relationship imply that there is a polynomial-time approximation algorithm with a constant approximation ratio for the clique problem? Justify your answer.