Subset Counting in Trees

Various enumeration problems for classes of simply generated families of trees have been the object of investigation in the past. We mention the enumeration of independent subsets, connected subsets or matchings for instance. The aim of this paper is to show how combinatorial problems of this type can also be solved for rooted trees and trees, which enables us to take better account of isomorphisms. As an example, we will determine the average number of independent vertex subsets of trees and binary rooted trees (every node has outdegree 2).

• Type: Journal
• Year: 2008
• Where: ARSCOM
• Authors: Stephan G. Wagner
• Keywords: ARSCOM 2008, Enumeration, Independent Subsets, Various Enumeration Problems