Matchings in starlike trees

AbstractLet m(G,k) be the number of k-matchings in the graph G. We write G1 ⪯ G2 if m(G1, k) ≤ m(G2, 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 T1 ⪯ T2 is shown to hold for various pairs of starlike trees T1, T2. The starlike trees (with a given number of vertices), extremal with respect to the relation ⪯, are characterized