The Number of Trees in a Network

1 September 1966

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuit Theory

Vol. 13 (3) , 271-281
https://doi.org/10.1109/TCT.1966.1082611

Abstract

In this paper we exhibit an explicit formula for the number of trees in a certain type of network. In particular, we define, in Definition 3, the concept of an incompletely partitioned network, and offer in Theorem 9 a formula for the number of trees of an incompletely partitioned network. Our formulas include, as special cases, the formulas exhibited previously in the literature by Weinberg [1] and Bedrosian [2].

Keywords

TREE GRAPHS
NETWORK SYNTHESIS
CIRCUIT THEORY
MATHEMATICS
NATIONAL ELECTRIC CODE
EIGENVALUES AND EIGENFUNCTIONS
CIRCUIT SYNTHESIS
PASSIVE NETWORKS
JOINING PROCESSES
CIRCUITS AND SYSTEMS

This publication has 2 references indexed in Scilit:

Formulas for the Number of Trees in a Network
IRE Transactions on Circuit Theory, 1961
A NOTE ON THE ENUMERATION AND LISTING OF ALL POSSIBLE TREES IN A CONNECTED LINEAR GRAPH
Proceedings of the National Academy of Sciences, 1954