Geometrical circuits of electrical networks

  title={Geometrical circuits of electrical networks},
  author={Ronald M. Foster},
  journal={Electrical Engineering},
IF ALL THE ELECTRICAL properties of a given electrical network are abstracted, there remains a geometric circuit completely characterized by the sets of branches terminating at the various vertexes. The use of such geometric circuits in place of the networks is desirable in the solution of a number of different problems. A successful application of this method requires to start with a complete enumeration of all distinct circuits classified according to certain specified properties. 

Some Topological Considerations in Network Theory

Elements of the theory of linear graphs which are readily applicable to communication theories are reviewed. These concepts are used to examine the geometrical significance of Kirchhoff's laws.

On a Problem of Network Topology

By this method, all the trees and fundamental circuit matrices may be determined and signs of cotree determinants and their minor determinants of a fundamental circuit matrix also may be easily determined.

Soul of circuit theory. A review on research activities of graphs and circuits in Japan

This paper reviews research activities in the area of topological aspects of circuit theory in Japan, most of which have been done after the previous report of H. Watanabe in the Special Centennial

Graph theory and electric networks

  • F. Harary
  • Mathematics
    IRE Trans. Inf. Theory
  • 1959
The treatment is expository, but introduces the unifying framework of graph theory for these various considerations, including hoff's Laws, mesh and node equations, and matrix tree theorem.

Networks, multipoles and multiports

  • A. Reibiger
  • Computer Science
    2013 European Conference on Circuit Theory and Design (ECCTD)
  • 2013
A general theory of the terminal behavior of multipoles is developed as the set of all signal pairs obeying its constitutive relation and both Kirchhoff's laws.

Search Strategies for Topological Network Optimization

An application of combinatorial search to the optimization of topologies in series-parallel networks and two complementary pruning techniques that bound the value of intermediate solutions from above and below are presented.

Interconnection Topologies and Routing for Parallel Processing Systems

A comparative survey of static interconnection topologies is given and the construction rules for various graphs are presented because these seemed along with the network characteristics most relevant for interconnecting processing.

Symmetry properties of graphs of interest in chemistry. III. Homotetrahedryl rearrangement

The symmetry properties of a graph representing rearrangement of homotetrahedryl cation C5H5+ initially introduced by Balaban are considered. The approach is based on the search for canonical



Maximum Output Networks for Telephone Substation and Repeater Circuits

Ideal telephone substation and repeater circuits are shown to present output and input requirements which can be met by a type of circuit containing four resistances, each of which has maximum

Non-Separable and Planar Graphs.

  • H. Whitney
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1931
A dual of a graph is defined by combinatorial means, and the paper ends with the theorem that a necessary and sufficient condition that a graph be planar is that it have a dual.