ELEMENTARY COMPLETE TREE TRANSFORMATION,
Abstract
It is known that a passive electrical network without mutual couplings can be analyzed by knowning all possible trees of a linear graph corresponding to the network. Since there exists a reasonably simple method of generating all possible trees of a linear graph without duplications, analysis of such a network by a computer becomes simple. When a pair of linear graphs is used, an active network can be analyzed by knowing all possible complete trees each of which is a tree of both linear graphs. At present there is no simple method of generating all possible complete trees without duplications. Hence, in order to obtain all possible complete trees by a computer, one of the best available methods at present is to generate all possible trees of each linear graph to obtain two collections of trees, then intersecting the two collections. It is not difficult to design an active network such that there are more than a thousand of trees in each of a pair of linear graphs corresponding to the net, but there are less than one hundred complete trees. Hence to obtain a simple method of generating all possible complete trees is undoubtedly important for analysis of active networks by a computer.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1965
- Accession Number
- AD0625201
Entities
People
- Wataru Mayeda
Organizations
- University of Illinois Urbana–Champaign