Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Camouflaging electrical $ 1$-networks as graphs

Author: Gabriel Kron
Journal: Quart. Appl. Math. 20 (1962), 161-174
MSC: Primary 94.30; Secondary 53.45
DOI: https://doi.org/10.1090/qam/148347
MathSciNet review: 148347
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Abstract: Lately it has become fashionable to develop the theory of electrical networks by starting first with a detailed, scholarly exposition of the theory of graphs (containing both nodes and branches), as given in textbooks on algebraic topology. However, when the graph analysis finally gets down to the study of actual electrically excited networks, it will invariably be found that all traces of the concepts of nodes and their associated ``incidence-matrices'' have disappeared from the final $ e = zi$ and other equations of state that are to be solved. In their place only the branches and the associated ``connection-matrices'' have been put to use, all still wrapped up however in an ill-fitting graph terminology. Of course such legerdemain had to be resorted to, since graph theorists happened to pick the wrong topological model for an electrical network. A graph possesses enough structure to propagate an electromagnetic wave and not an electrical current.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/148347
Article copyright: © Copyright 1962 American Mathematical Society

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