Cut-set graph and systematic generation of separating sets
- 1 May 1972
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuit Theory
- Vol. 19 (3) , 233-240
- https://doi.org/10.1109/tct.1972.1083456
Abstract
In this paper an efficient method of generating separating sets of a given graph with the use of a newly defined concept-a cutset graph-is discussed. The cut-set graph of a given graphGis defined such that each edge of the graph corresponds to a pair of basic branch cut-sets ofGhaving the relation that the ring sum of these cut-sets coincides with an incident cut-set with respect to a vertex inG. The present paper shows that the cut-set graph is a useful tool for solution of the problem of generating all of the basic vertex cut-sets and the basic mixed cut-sets of a given graph.Keywords
This publication has 8 references indexed in Scilit:
- Planar GraphsPublished by Springer Nature ,1992
- The Algebra of Sets of Trees, k-Trees, and Other ConfigurationsIEEE Transactions on Circuit Theory, 1968
- Proper flow paths in vertex-weighted communication netsProceedings of the Institution of Electrical Engineers, 1968
- On the Smallest Disconnecting Set in a GraphIEEE Transactions on Circuit Theory, 1968
- Topological Analysis and Synthesis of Communication NetworksPublished by Columbia University Press ,1962
- A generalization of the cut-setJournal of the Franklin Institute, 1962
- Graphs with two kinds of elementsJournal of the Franklin Institute, 1960
- The path matrix and switching functionsJournal of the Franklin Institute, 1959