On the Graphicity of the Independence Structure of Linear Active Networks

Authors

  • Csongor Gy. Csehi
    Affiliation
    Department of Computer Science and Information Theory, Faculty of Electrical Engineering and Informatics, Budapest University of Techology and Economics, Hungary
  • András Recski
    Affiliation
    Department of Computer Science and Information Theory, Faculty of Electrical Engineering and Informatics, Budapest University of Techology and Economics, Hungary
https://doi.org/10.3311/PPee.9982

Abstract

Consider a linear network composed of 2-terminal devices. Its interconnection structure is described by a graph G. The voltages or the currents of a subset of devices can independently be prescribed if and only if the subset of the corresponding edges in the graph G is circuit-free or cut set free, respectively.  This classical result of Kirchhoff can be generalized for networks containing multiterminal devices as well: the independence structure can be described by the circuits and cut sets of a more general abstract mathematical structure, a matroid M. However, these matroids will not always be graphic. Using some recent mathematical results for characterizing graphic structures among the matroids, here we give a physical characterization of subclasses of those active networks where M happens to be graphic.

Keywords:

matroid theory, linear network, multiterminal devices

Citation data from Crossref and Scopus

Published Online

2017-05-05

How to Cite

Csehi, C. G., Recski, A. “On the Graphicity of the Independence Structure of Linear Active Networks”, Periodica Polytechnica Electrical Engineering and Computer Science, 61(2), pp. 193–197, 2017. https://doi.org/10.3311/PPee.9982

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Articles