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The connectivity function of a graph

Published online by Cambridge University Press:  26 February 2010

Lowell W. Beineke  and
Frank Harary
Lowell W. Beineke
Affiliation:
Purdue University, Fort Wayne. University of Michigan, Ann Arbor.
Frank Harary
Affiliation:
Purdue University, Fort Wayne. University of Michigan, Ann Arbor.
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Extract

The vertex-connectivity and the edge-connectivity of a graph involve minimum sets of vertices and edges, respectively, whose removal results in a disconnected graph. However, the mixed case of separating sets consisting of both vertices and edges appears to have been overlooked. Such considerations might apply to vulnerability problems, such as that of disrupting a railway network with both tracks and depots being destroyed. Depending on the relative costs, a particular combination of tracks and depots might be optimal for the purpose.

Type
Research Article
Information
Mathematika , Volume 14 , Issue 2 , December 1967 , pp. 197 - 202
Copyright
Copyright © University College London 1967

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References

1.Dirac, G. A., “Short proof of Menger's graph theorem”, Mathematika, 13 (1966), 42–44.CrossRefGoogle Scholar
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4.Menger, K., “Zur allgemeinen Kurventheorie”, Fund. Math., 10 (1927), 96–115.CrossRefGoogle Scholar