Enumeration of externally labelled trees

Abstract

We enumerate a special clws of trees, called externally labelled trea. This is done by formulating a recursion relation in two variable, the number of internal Lines, i, and the number of exted lines, n, for these tress, and subsequently solving it. The solutbn is discussed in detail. In particular we consider the case where n becomes large. while summing on i. The extemdy labelled trees considered correspond to the Feymn diagrams one encounters in perturbation theolies for fundamental forces, involving one type of partide that self-interacts.