Matchings in starlike trees

Let m(G, k) be the number of k-matchings in the graph G. We write G(1) less than or equal to G(2) if m(Gj, k) less than or equal to m(G(2), k) for all k = 1,2,.... A tree is said to be starlike if it possess. es exactly one v ertex of degree greater than two. The relation T-1 less than or equal to T- 2 is shown to hold for various pairs of starlike trees T-1,T-2. The starlik e trees (with a given number of vertices), extremal with respect to the rel ation less than or equal to, are characterized. (C) 2001 Elsevier Science L td. All rights reserved.