The (upper) matching number ν(G) of graph G, sometimes known as the edge independence number, is the size of a maximum independent edge set. Equivalently, it is the degree of the matching-generating polynomial M(x) = sum_(k = 0)^(ν(G)) Φ_k x^k where Φ_k is the number of k-matchings of a graph G. The notations c(G), ρ_s(G), or α'(G) are sometimes also used. The matching number is also the size of a largest maximal independent edge set, while the size of a smallest maximal independent edge set is called the lower matching number.
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