Generation and Realization of Trees and k-Trees

In this paper we consider an analysis-synthesis problem in graph theory. The analysis problem is that of efficient generation of trees, 2-trees, and
k
-trees of a given "labeled" graph. The synthesis problem is that of finding a graph that realizes a given set of trees, 2-trees, or realizes given sets of trees and 2-trees simultaneously. These results have a strong bearing upon topological analysis and synthesis of electrical networks.