text: A quantity with this name is the dimension of a vector space over a given field.
full_question: A quantity with this name is the dimension of a vector space over a given field. That quantity measures the relative size of a field extension. Finite undirected graphs all have an even number of vertices with an odd value of this quantity according to the handshaking lemma, and a graph's total value of this quantity is equal to two times the number of edges. The Abel-Ruffini theorem states that five is the lowest value of another quantity of this name that produces equations with no radical solutions. For cubic polynomials, that quantity is equal to three. For 10 points, give this name of several quantities in mathematics, which for polynomials is the value of the highest exponent.
first_sentence: A quantity with this name is the dimension of a vector space over a given field.
raw_answer: degree