Geometrical circuits of electrical networks

@article{Foster1932GeometricalCO,
  title={Geometrical circuits of electrical networks},
  author={Ronald M. Foster},
  journal={Electrical Engineering},
  year={1932},
  volume={51},
  pages={43-43}
}
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. 

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References

SHOWING 1-2 OF 2 REFERENCES

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
TLDR
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.