Abstract
Let m( G,k) be the number of k-matchings in the graph G. We write G 1 ⪯ G 2 if m( G 1, k) ≤ m( G 2, k) for all k = 1, 2,…. A tree is said to be starlike if it possesses exactly one vertex of degree greater than two. The relation T 1 ⪯ T 2 is shown to hold for various pairs of starlike trees T 1, T 2. The starlike trees (with a given number of vertices), extremal with respect to the relation ⪯, are characterized.
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